Appropriate patients will be enrolled in a 3+3 alternating dose escalating fashion, to a maximum dose of niraparib of 300mg daily and a maximum dose of carboplatin area under the curve (AUC) of 4. The 3+3 schema will be employed to insure safety and tolerability. However, within any given cohort, a full contingent of 6 patients (assuming adequate tolerability) will be enrolled to capture a sufficient number of patients and samples for pharmacodynamic assessment of DNA damage.