Vorinostat, Carboplatin and Gemcitabine in Women With Recurrent, Platinum-Sensitive Ovarian Cancer

Inclusion Criteria: * Histologically confirmed recurrent epithelial ovarian cancer, fallopian tube cancer, or peritoneal cancer * Must have received a platinum-based chemotherapy regimen at initial diagnosis * Patients with primary platinum-sensitive (defined as a cancer initially platinum-sensitive followed by a progression-free interval from first exposure to platinum of 6 months or greater) recurrent ovarian, tubal or peritoneal cancer * Must have an elevated CA125 (twice the ULN) within 2 weeks of enrolling on study (2 pretreatment measurements that are twice the upper limits of institutional normal and are drawn at least 1 day but not more than 14 days apart). At least one of the samples should be checked within one week of starting treatment. Measurable cancer via RECIST criteria via CT or MRI scan is not required but if clinically indicated will be monitored. * For patients who do not have an elevated CA125 (twice the ULN), participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as 20mm or greater with conventional techniques or as 10mm or greater with spiral CT scan. * 18 years of age or older * Life expectancy of greater than 16 weeks * ECOG Performance Status 0, 1, or 2 * Participants must have normal organ and marrow function as outlined in the protocol * Patients could have received up to 1 prior non-platinum chemotherapy regimen in the recurrent setting (anti-angiogenic agents and other phase II non-hormonal therapies used to treat recurrent cancer count as a prior non-platinum therapy) but only one prior platinum (used to treat initial diagnosis). Patients may received up to 2 prior hormonal therapies. * Women of child-bearing potential must agree to use adequate contraception prior to study entry and for the duration of study participation * Must be able and willing to take oral medications * No clinical nor radiographic evidence of an existing or impending bowel obstruction * Should be at least 2 weeks from any surgical procedure, with the exception of minor surgery, such as port placement * Patients who have known carboplatin hypersensitivity reaction can receive carboplatin if they are followed by an allergist, follow a published hypersensitivity desensitization protocol when receiving carboplatin, and agree to receive carboplatin under these circumstances * Patients taking valproic acid for epilepsy may enroll if they discontinue valproic acid 30 days prior to enrolling for washout * Patients must have a normal QTc interval and no history of QTc prolongation on EKG Exclusion Criteria: * Chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * May not be receiving any other investigational agent * Participants with known brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, pulmonary disease, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or breastfeeding women * Individuals with a history of different malignancy are ineligible except for the following circumstances: disease-free for at least 5 years and are deemed by the investigator to be a low risk for recurrence of that malignancy; cervical cancer in situ, concurrent stage IA and grade I endometrial cancer, and basal cell or squamous cell carcinoma of the skin * Patients taking valproic acid unless valproic acid is stopped at least 30 days prior to enrollment * Receipt in the past of any other HDAC inhibitor for treatment of any malignancy * Receipt of radiation therapy to \>25% of bone marrow-bearing areas * Patients who have gastrointestinal disorders likely to interfere with absorption of vorinostat * Known active HIV or hepatitis viral infection