Inclusion Criteria:

• Patient has signed the Informed Consent (ICF) prior to any screening procedures being performed and is able to comply with protocol requirements. 
• Age > 18 years at time of study entry. 
• Willingness and ability to comply with study and follow-up procedures. 
• Histological confirmation of diagnosis of low-grade serous carcinoma of ovary, fallopian tube or peritoneum; original diagnosis of de novo low-grade serous carcinoma or original diagnosis of serous borderline tumor with subsequent diagnosis of low-grade serous carcinoma:
  • In order to prevent inclusion of patients with high-grade serous carcinoma, diagnosis of low-grade serous carcinoma will be verified as part of screening review by a gynecologic pathologist. Tissue for confirmation can be from primary tumor or recurrence.
• Patient must have recurrent, measurable disease by RECIST v1.1. 
• There are no restrictions on number of prior therapies. 
• Patient cannot have previously received a prior cyclin dependent kinase inhibitor (CDKi). Patients who were treated with letrozole or another aromatase inhibitor for other indications must have not taken the drug for 6 months prior to initiating letrozole for this trial and may not have progressed on treatment.
• Patients must not have remaining ovarian function to be included. In women who have at least one retained ovary, menopause must be confirmed with laboratory confirmation. Women who have ovarian function are eligible but must be placed on hormonal suppression. Menopause must be confirmed with laboratory confirmation, to include an estradiol level as this is assessed within 8 weeks of patient having been on tamoxifen. 
• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2.
• Resolution of all acute toxic effects of prior therapy or surgical procedures to National Cancer Institute (NCI) CTCAE Grade ≤ 1. 
• Patient has adequate bone marrow and organ function as defined by the following laboratory values at screening:
  • Absolute neutrophil count ≥ 1.5 × 10^9/L;
  • Platelets ≥ 100 × 10^9/L;
  • Hemoglobin ≥ 9.0 g/dL;
  • Potassium, total calcium (corrected for serum albumin), magnesium, sodium and phosphorus within normal limits for the institution or corrected to within normal limits with supplements before first dose of study medication;
  • INR ≤ 1.5;
  • Serum creatinine < 1.5 mg/dL or creatinine clearance ≥ 50 mL/min;
  • In the absence of liver metastases, alanine aminotransferase (ALT) and aspartate aminotransferase (AST) < 2.5 x ULN. If the patient has liver metastases, ALT and AST < 5 x ULN;
  • Total bilirubin < ULN or total bilirubin ≤ 3.0 x ULN or direct bilirubin ≤ 1.5 x ULN in patients with well-documented Gilbert's Syndrome.
• Patient with available standard 12-lead ECG with the following parameters at screening: 
  • QTcF interval at screening < 450msec (using Fridericia's correction);
  • Resting heart rate 50-90 bpm.
• Must be able to swallow ribociclib and letrozole capsules/tablets.
• Patients receiving tamoxifen or toremifine must have washout period of 5 half-lives prior to randomization.

Exclusion Criteria:

• Patient has a known hypersensitivity to any of the excipients of ribociclib or letrozole. 
• Patient has a concurrent malignancy or malignancy within 3 years prior to starting study drug, with the exception of adequately treated, basal or squamous cell carcinoma, non-melanomatous skin cancer or curatively resected cervical cancer. Patients with known brain metastases are excluded.
• Patients with central nervous system (CNS) involvement unless they meet ALL of the following criteria:
  • At least 4 weeks from prior therapy completion (including radiation and/or surgery) to starting the study treatment;
  • Clinically stable CNS tumor at the time of screening and not receiving steroids and/or enzyme inducing anti-epileptic medications for brain metastases.
• Patient has impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection).
• Patient has a known history of HIV infection (testing not mandatory).
• Patient has any other concurrent severe and/or uncontrolled medical condition that would, in the investigator’s judgment, cause unacceptable safety risks, contraindicate patient participation in the clinical study or compromise compliance with the protocol (e.g., chronic pancreatitis, chronic active hepatitis, active untreated or uncontrolled fungal, bacterial or viral infections, etc.). 
• Clinically significant, uncontrolled heart disease and/or cardiac repolarization abnormalities, including any of the following:
  • History of acute coronary syndromes (including myocardial infarction, unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting) or symptomatic pericarditis within 6 months prior to screening;
  • History of documented congestive heart failure (New York Heart Association functional classification III-IV);
  • Documented cardiomyopathy;
  • Left Ventricular Ejection Fraction (LVEF) < 50% as determined by Multiple Gated acquisition (MUGA) scan or echocardiogram (ECHO);
  • Clinically significant cardiac arrhythmias (e.g., ventricular tachycardia), complete left bundle branch block, high-grade AV block (e.g., bifascicular block, Mobitz type II and third degree AV block);
  • Long QT syndrome or family history of idiopathic sudden death or congenital long QT syndrome, or any of the following: 
    • Risk factors for Torsades de Pointe (TdP) including uncorrected hypocalcemia, hypokalemia or hypomagnesemia, history of cardiac failure, or history of clinically significant/symptomatic bradycardia;
    • Concomitant use of medication(s) with a known risk to prolong the QT interval and/or known to cause Torsades de Pointe that cannot be discontinued (within 5 halflives or 7 days prior to starting study drug) or replaced by safe alternative medication;
    • Inability to determine the QT interval on screening (QTcF, using Fridericia’s correction);
    • Systolic blood pressure (SBP) >160 mmHg or <90 mmHg at screening;
• Patient is currently receiving any of the following medications and cannot be discontinued 7 days prior to starting study drug:
  • Known strong inducers or inhibitors of CYP3A4/5, including grapefruit, grapefruit hybrids, pummelos, star-fruit, and Seville oranges;
  • That have a narrow therapeutic window and are predominantly metabolized through CYP3A4/5;
  • Herbal preparations/medications, dietary supplements.
• Participation in other studies involving investigational drug(s) within 30 days prior to randomization or within 5 half-lives of the investigational product (whichever is longer) or participation in any other type of medical research judged not to be scientifically or medically compatible with this study. If the patient is
  enrolled or planned to be enrolled in another study that does not involve an investigational drug, the agreement of Novartis study medical lead is required to establish eligibility.
• Patient is currently receiving warfarin or other coumadin-derived anticoagulant for treatment, prophylaxis or otherwise. Therapy with heparin, low molecular weight heparin (LMWH) or fondaparinux is allowed. Direct-Acting Oral Anticoagulants (DOACS) are permitted. 
• Patient is currently receiving or has received systemic corticosteroids ≤ 2 weeks prior to starting study drug, or who have not fully recovered from side effects of such treatment. The following uses of corticosteroids are permitted: a short duration (<5 days) of systemic corticosteroids; any duration of topical applications (e.g., for rash), inhaled sprays (e.g., for obstructive airways diseases), eye drops or local injections (e.g., intra-articular).
• Patient who has received radiotherapy ≤ 4 weeks or limited field radiation for palliation ≤ 2 weeks prior to starting study drug, and who has not recovered to grade 1 or better from related side effects of such therapy (exceptions include alopecia) and/or in whom ≥25% of the bone marrow (Ellis, 1961) was irradiated.
• Patient has had major surgery within 14 days prior to starting study drug or has not recovered from major side effects (tumor biopsy is not considered as major surgery).
• Patient with a Child-Pugh score B or C.
• Patients who are pregnant or breastfeeding. 
• Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, unless they are using highly effective methods of contraception throughout the study and for 3 weeks after study drug discontinuation. Highly effective contraception methods include:
  • Total abstinence when this is in line with the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of
    contraception;
  • Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy), total hysterectomy, or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment.
• Women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g., age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential.
• Current use of food or drugs known to be potent CYP3A4 inhibitors, drugs known to be potent CYP3A4 inducers, and drugs that are known to prolong the QT interval unless the prohibited concomitant medication can be replaced by other drugs of less potential to inhibit or induce CYP3A4 or prolong QT interval
• Patients whose tumors contain both low-grade serous carcinoma (LGSC) and high-grade serous carcinoma (HGSC).
• Patients with history of haemopoietic stem cell or bone marrow transplant.