All subjects will be treated with an intravenous infusion of the experimental drug (Bevacizumab 15 mg/kg) every 3 weeks for a total of twelve (12) weeks on study. The primary endpoint will be time to the need for repeat abdominal paracentesis after the start of therapy. Secondary endpoints will include an analysis of the mean number of paracenteses required in each subject over the course of 3 months, determination of the repeat paracentesis response rate (proportion of subjects who have a doubling in baseline time to repeat paracentesis) and an assessment of the effect of treatment on quality of life using a subject questionnaire.