Brief Summary: This early phase I trial studies how well olaparib works in treating patients with newly diagnosed BRCA-mutant ovarian, primary peritoneal, or fallopian cancer before surgery. Olaparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the feasibility of daily olaparib given in the neoadjuvant setting in women with primary advanced high grade non-mucinous epithelial ovarian, fallopian tube, or primary peritoneal cancer. SECONDARY OBJECTIVES: I. Estimate efficacy of olaparib given in the neoadjuvant setting using response rate (by Response Evaluation Criteria in Solid Tumors \[RECIST\] in subjects with measurable disease). II. Estimate proportion of subjects able to proceed immediately to interval tumor reductive surgery (without chemotherapy). III. Determine progression-free survival (PFS). IV. Determine complete pathologic response rate at the time of surgery. V. Determine the toxicity of daily olaparib given in the neoadjuvant setting. VI. Evaluate the toxicity of chemotherapy given after neoadjuvant olaparib. VII. Measure longitudinal symptom burden of study subjects treated with neoadjuvant olaparib and chemotherapy after olaparib. EXPLORATORY OBJECTIVES: I. Explore deoxyribonucleic acid (DNA) copy number and level of ribonucleic acid (RNA) and protein expression in homologous recombination-related pathways before and after treatment with olaparib in women with primary advanced high grade non-mucinous epithelial ovarian, fallopian tube, or primary peritoneal cancer. II. Correlate molecular results to clinical endpoints including response and survival. OUTLINE: Patients receive olaparib orally (PO) twice daily (BID) on days 1-28. Treatment repeats every 28 days for up to 2 cycles in the absence of disease progression or unacceptable toxicity. After treatment, patients either undergo surgery then receive standard chemotherapy for up to 4 cycles or receive standard chemotherapy within 14 days for up to 4 cycles then undergo surgery in the absence of disease progression or unacceptable toxicity at the discretion of the treating physician. After completion of study treatment, patients are followed up at 30 days.