A Study of Rucaparib Administered With Radiation in Patients With Triple Negative Breast Cancer With an Incomplete Response Following Chemotherapy

Inclusion Criteria: * Female, ≥ 18 years of age. * Non-metastatic, histologically or cytologically-confirmed TNBC (defined as ER \<1%, PR \<1%, her-2-neu 0-1+ by IHC or FISH-negative or as per MD discretion), with evidence of residual disease in the breast or lymph nodes after neoadjuvant chemotherapy, at the time of definitive surgical treatment. * Non-metastatic, histologically or cytologically-confirmed hormone-receptor positive, Her2/neu negative breast cancer (defined as ER \>1% or PR \>1% AND Her-2/neu 0-1+ by IHC or FISH-negative, or as per MD discretion), with evidence of residual grade 3 invasive breast cancer AND either 1) \>5 cm of residual disease in the breast OR 2) ≥ 4 axillary LNs in the axilla after neoadjuvant chemotherapy, at the time of definitive surgical treatment. * Definitive surgical treatment with breast-conserving surgery or mastectomy and axillary lymph node evaluation. * At least 6-month life expectancy, ECOG Performance status \< 2. * Willingness to discontinue any cytotoxic chemotherapeutic agents, and biologic therapy at least 2 weeks prior to the start of RT. * Adequate organ function (assessed within 30 days prior to initiation of protocol treatment, unless otherwise indicated) as follows: Hematology * Absolute Neutrophil Count (ANC) ≥1500/mm\^3 * Platelet Count ≥100,000/mm\^3 * Hemoglobin ≥9.0 g/dL (after transfusion if required) Renal Function * Creatinine Serum ≤ 1.5 mg/dL or Creatinine Clearance ≥ 45 mL/min\^a Hepatic Function * Bilirubin ≤ 1.5 mg/dL * Aspartate Aminotransferase (AST) ≤ 2.5 x ULN\^b * Alanine Aminotransferase (ALT) ≤ 2.5 x ULN ULN = upper normal limit of institution's normal range 1. If calculated creatinine clearance is \< 45mL/min, a 24-hour urine collection for creatinine clearance may be performed 2. Subjects with documented Gilbert's disease may have bilirubin up to 2.5 mg/dL * Negative serum pregnancy test within 14 days prior to study treatment if a woman has child-bearing potential. Subjects of child bearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. * Ability to swallow and retain oral medications. * Written informed consent obtained from subject and ability for subject to comply with the requirements of the study. * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the duration of study participation. Should a woman become pregnant while participating on study, she should inform the treating physician immediately. Exclusion Criteria: * Gross residual tumor on imaging or positive margins after breast conserving surgery that are un-excised, as radiation dose in the study will be limited to 60 Gy. * Complete pathologic response to NAC. * Receipt of PARP inhibitor prior to RT. * Pregnant or expecting to conceive within the projected duration of the trial, starting with screening visit through 180 days after the last dose of trial treatment. * Prior history of radiation therapy to the ipsilateral breast and/or regional nodes is not allowed (prior RT to other sites is permitted). * Patients with breast augmentation implants are excluded. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to rucaparib. * Concomitant anti-neoplastic treatment is not allowed during protocol treatment and should be completed at least 2 weeks prior to commencement of protocol treatment, with resolution of associated acute toxicities. Bisphosphonates are permitted without restriction even during protocol treatment. Maintenance pembrolizumab is permitted during the protocol treatment. * Significant comorbidity: Patients with clinically significant and uncontrolled major disease or disorder that could exacerbate potential toxicities, confound safety assessments, require excluded therapy for management, or limit study compliance. * Ongoing therapy with other investigational agents. Patients may not be receiving any other investigational agents. * Unresolved toxicity from other agents. Patients with unresolved CTCAE v4.03 Grade 3 or greater toxicity from prior administration of another investigational drug and/or anti-cancer treatment are not eligible.