The investigators hypothesize that 12 weeks of treatment with varenicline, a partial nicotinic acetylcholine receptor agonist will be more effective than placebo in treating tobacco dependence and reducing nicotine withdrawal symptoms in currently drinking alcoholic smokers. The investigators will also explore whether varenicline has an effect on drinking behavior among currently drinking alcoholics. The investigators propose the following specific aims to test these hypotheses in 70 currently drinking alcoholic smokers recruited at the Mayo Clinic in Rochester, Minnesota.