This is a small 12-week placebo-controlled pilot study examining tolerability and potential efficacy in anticipation of a larger, placebo-controlled trial of zonisamide for treatment of alcohol dependence. It is a randomized, double-blind trial of zonisamide vs. placebo at flexible dosages of 100-500mg/day in alcoholics receiving ambulatory psychosocial treatment. Participants will take part in six individual Cognitive-Behavioral based therapy sessions, which are focused on learning coping skills. Participants must endorse a goal of either cutting down their drinking to non-hazardous levels, or abstinence.