Inclusion Criteria: - PRE-REGISTRATION INCLUSION CRITERIA - Smoking history of >= 30 pack‐years AND either current smoker (still smoking or quit < 1 year prior to pre‐registration) OR former smoker (quit 1‐15 years prior to pre‐registration); Note: Pack years is determined by multiplying the number of packs smoked per day by the number of years smoked - Eastern Cooperative Oncology Group (ECOG) performance status =< 1 - Computed tomography (CT) scan of the chest done =< 6 months prior to pre‐registration showing either negative findings (no nodules) or solid or part‐solid nodules < 6 mm in size (consistent with < 1% probability of malignancy, Lung‐Reporting and Data Systems [RADs] version 1.0) - Willingness to employ adequate contraception, if applicable; Note: women of child‐bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her study physician immediately - Ability to understand and the willingness to sign a written informed consent document - REGISTRATION INCLUSION CRITERIA - Leukocytes (white blood cell [WBC]) >= 3,000/microliter - Neutrophils (absolute neutrophil count [ANC]) >= 1,500/microliter - Platelets >= 100,000/microliter - Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) Note: Higher total bilirubin levels (=< 3 mg/dL) can be allowed if due to known benign liver condition, i.e. Gilbert''s - Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT]) =< 1.5 x institutional upper limit of normal (ULN) - Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 1.5 x institutional upper limit of normal (ULN) - Creatinine =< institutional upper limit of normal (ULN) Exclusion Criteria: - PRE-REGISTRATION EXCLUSION CRITERIA - History of any malignancy; exceptions: non‐melanoma skin cancer or carcinoma in situ (CIS) of the cervix - Known hepatitis B or C - Receiving any other investigational agents - Any prior investigational immune therapy, such as for lung cancer prevention or treatment or for CIS of the cervix - Use of oral or systemic steroids or other systemic anti‐immune therapy =< 90 days prior to pre-registration; Note: Use of inhaled/nasal steroids and local steroid injections for pain control are not exclusionary - Known human immunodeficiency virus (HIV) - Known autoimmune disease - Known non‐alcoholic steatohepatitis (NASH) or non‐alcoholic fatty liver disease (NAFLD) - History of allergic reactions attributed to compounds of similar chemical or biologic composition to MUC1/Poly‐ICLC - Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements - REGISTRATION EXCLUSION CRITERIA - Any positive antinuclear antibody (ANA) titer above 1:160, even in an asymptomatic individual. Note: Weakly positive ANA defined as ANA titers up to 1:160 maximum (=< 1:160) will be acceptable in an asymptomatic individual who is otherwise eligible for the study - Pregnant or breast feeding; Note: Pregnant women are excluded from this study because the MUC1/Poly-ICLC vaccine may have the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events (AEs) in nursing infants secondary to treatment of the mother with MUC1/Poly-ICLC vaccine, breastfeeding should be discontinued if the mother is treated with the vaccine