The purpose of this study is to learn whether ondansetron and topiramate either alone or in combination is safe and effective in the treatment of alcohol dependence. This 13 week out-patient clinical trial is randomized, double-blind, and placebo-controlled. There are post-study follow up visits 1, 2 and 3 months after the end of the study. Participants will receive ondansetron and topiramate either alone or in combination or a placebo coupled with psychotherapy.