Inclusion Criteria:

        A patient will be eligible for androgen receptor expression testing (STEP 1) if the
        following criteria are met:

          -  Female

          -  Pathologically confirmed invasive cancer of the breast

          -  ER/PR status (ER or PR defined as positive if ≥1%; ER/PR is defined as negative if
             <1%):

          -  Phase I: Patients may have ER/PR(-) breast cancer.

          -  HER2 normal (IHC 0-1; FISH < 2.0)

          -  Non-measurable or measurable, metastatic disease

          -  Available tissue for AR testing for research purposes

        A patient will be eligible for participation in the therapeutic trial (STEP 2) if the
        following criteria are met:

          -  Androgen receptor expression testing confirms that the patient's tumor is AR (+). AR
             is considered positive if ≥1% of cell nuclei are immunoreactive using the Dako
             antibody (clone AR441). Receptor testing may be performed on either primary tumor
             specimen or tissue from a metastatic site. Local testing permitted for eligibility but
             will require confirmation at MSKCC.

          -  There is no limit to the number of prior chemotherapy or endocrine therapy regimens
             allowed. Patients with ER(+) AR(+) breast cancer must have had at least 1 prior line
             of endocrine therapy to be eligible for the phase I portion of the trial.

          -  At least 2 weeks since last cytotoxic chemotherapy, hormonal therapy, or radiotherapy.
             Toxicities related to prior therapy must either have returned to grade 1, or baseline
             (excluding alopecia)

          -  Patient may receive bisphosphonates/denosumab for the palliation of bone metastases

          -  If patient has a history of brain metastases or leptomeningeal disease, lesions must
             be stable for at least 3 months (as documented by either head CT or brain MRI)

          -  Prior treatment with bicalutamide will not be allowed

          -  At least 3 weeks from major surgery with full recovery

          -  ECOG performance status 0-2

          -  Age 18 years or greater

          -  Postmenopausal. Use of LHRH agonist permitted.

          -  Patients must not have another, non-breast, active malignancy that requires treatment.

          -  The effects of palbociclib on the developing human fetus at the recommended
             therapeutic dose are unknown. Women of child-bearing potential must agree to use
             adequate contraception (barrier method of birth control; abstinence). Women must not
             breast feed while on study.

          -  Ability to understand and the willingness to sign a written informed consent document.

          -  Ability to swallow intact palbociclib capsules and bicalutamide tablets.

          -  Adequate organ and marrow function as defined below (ULN indicates institutional upper
             limit of normal):

               -  Absolute neutrophil count ≥ 1.5 10^9/

               -  Hemoglobin ≥ 9.0 g/dL

               -  WBC ≥ 3.0 10^9/L

               -  Platelets ≥ 100 10^9/L

               -  Total bilirubin ≤ 1.5 ULN except for patients with known Gilbert syndrome

               -  AST(SGOT)/ALT(SGPT) ≤ 3 institutional ULN

               -  Plasma creatinine ≤ 1.5 ULN or Creatinine Clearance > 50 mL/min (calculated by
                  Cockcroft-Gault method)

               -  QTc interval ≤ 470 msec

        Exclusion Criteria:

          -  Patients who have not recovered from adverse events of prior therapy to ≤ NCI
             CTCAEv4.0 Grade 1.

          -  Patients receiving any other investigational anti-cancer agents.

          -  Patients who have received prior treatment with a selective CDK4/6 inhibitor

          -  Patients who have received prior anti-androgen therapy

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to palbociclib.

          -  Uncontrolled intercurrent illness including, but not limited to, known ongoing or
             active infection, including HIV, active hepatitis B or C, symptomatic congestive heart
             failure, unstable angina pectoris, cardiac arrhythmia (specifically, uncontrolled
             atrial fibrillation or ventricular dysrhythmias except ventricular premature
             contractions), or psychiatric illness/social situations that would limit compliance
             with study requirements.

          -  Pregnant women and women who are breast-feeding.

          -  Patients with a history of long-QT syndrome or documented family history of long-QT
             syndrome. Patients who must remain on drugs that prolong the QT interval.

          -  Palbociclib is a substrate of CYP3A. Caution should be exercised when dosing
             palbociclib concurrently with CYP3A inducers or inhibitors. Furthermore, patients who
             are taking concurrent medications that are strong inducers/inhibitors or substrates of
             CYP3A4 should be switched to alternative medications to minimize any potential risk.