• Bone marrow aspirate after completion of all definitive therapy demonstrates detectable DTCs (via IHC) as performed by central laboratory assessment at University of Pennsylvania.

• History of stage II-III histologically-confirmed ER+/Her2 neg invasive breast cancer with no evidence of recurrent local or distant disease (by American Joint Committee on Cancer 7th edition). Patients with bilateral breast cancer are eligible, so long as both cancers are ER+/Her2 neg, at least one meets other eligibility criteria and patient is treated with curative intent. For patients who undergo neoadjuvant therapy, eligibility is based upon pathologic stage of residual disease at surgery.

• ER+/Her2 neg receptor status on breast primary tumor (by American Society of Clinical Oncology/College of American Pathologists guidelines). Any partial response (PR) status is allowed. Tumors that are ER negative and PR positive are not eligible. Patients who undergo neoadjuvant therapy are eligible if either the pre-treatment biopsy or residual disease at surgery is ER+/Her2 neg.

• Patients must have completed all primary and adjuvant therapy (including surgery, chemotherapy, and radiation) with the exception of adjuvant endocrine therapy. Prior treatment-related toxicity must be resolved to ≤ Grade 1 with the exception of alopecia and peripheral neuropathy, prior to study enrollment.

• Patients may have received prior CDK4/6 inhibitor therapy with an agent other than Palbociclib. Patients must have discontinued CDK4/6 inhibitor at least 6 months prior to screening.

• Patients must be receiving adjuvant endocrine therapy at the time of enrollment. Patients are eligible to enroll within 2-7 years after initiation of adjuvant endocrine therapy. Use of tamoxifen as adjuvant endocrine therapy during study treatment is not allowed on hydroxychloroquine arms due to the potential drug-drug interaction with hydroxychloroquine. However, patients on tamoxifen at the time of screening may enroll on the treatment trial if switched to an aromatase inhibitor at least 21 days prior to starting study therapy in the event patient is randomized to a hydroxychloroquine containing arm. Premenopausal patients on concurrent ovarian suppression are eligible. Patients on any other adjuvant endocrine therapy, including any investigational therapy, are ineligible.

• Patients receiving bone modifying agents (bisphosphonates or rank-ligand inhibitors) at the time of screening may continue this therapy. Bone modifying agents may not be initiated while receiving study treatment.

• No concurrent enrollment on another investigational therapy clinical trial.

• Men and women, age ≥ 18 years.

• No contraindications to the study medications (refer to Section 7.2) or uncontrolled medical illness.

• Adequate bone marrow, liver, and renal function and other parameters.

• Ability to speak and understand English