There's no single alcoholism gene yet isolated, but there are personality types that are more susceptible to alcoholism and genetic mental disorders that predispose people to self medicate with alcohol.
As with most things, there's no polarized nature vs nurture, but a combination of the two. Nurture certainly comes into play with there being a higher familial rate of alcoholism and other addictions since addicted parents hardly ever provide an emotionally healthy home life for their children.
@911 mentioned alcoholism skipping a generation. I'm interested in the book he referenced. From what I've read and observed through the years, a child of an alcoholic can choose a life of sobriety but not deal with the underlying patterns of family dysfunction which can set the next generation up for substance abuse.
@mrstime Were any of your grandparents alcoholics?