Patients receive paclitaxel IV over 3 hours, carboplatin IV over 15-30 minutes, and bevacizumab IV over 90 minutes on day 1 and oral hydroxychloroquine on days 1-21. Treatment repeats every 21 days for a total of 4 courses. Patients then receive bevacizumab IV over 30-90 minutes every 21 days and oral hydroxychloroquine daily for up to 1 year in the absence of disease progression or unacceptable toxicity.