 In this study the influence of zonisamide administration over a 13 week period on alcohol consumption in alcoholic alcohol dependent subjects will be examined. The dose of zonisamide given to subjects will be slowly increased over a period of several weeks. They will receive a full dose over a 5 week period. This will be a pilot study in which all of the subjects will only receive zonisamide. A primary objective of this study is to determine the possible size of the effect that zonisamide administration has on drinking i.e. drinks consumed per day to allow us to plan for a larger clinical trial of the effects of zonisamide on alcohol dependence. 