"I HAVE had my green card for the past six years. I obtained it through my job. I would like to apply for U.S. citizenship but I think there could be a problem. I have a DUI conviction that I received last year. I was pulled over for reckless driving. No one was injured. This was my only brush with the law since being in America, but I'm reluctant to go forward with getting citizenship because of it. I am also in Alcoholics Anonymous, and I'm doing well but afraid that this also would be seen as a strike against me. I regret very much what happened. I guess I'll have to speak to a lawyer, but I wanted to get an opinion first. What should I do?"
YES, you are correct in stating that it would be best to consult an immigration attorney prior to proceeding with naturalization, but in all likelihood, given the information that you've provided, your single DUI conviction will not preclude you from becoming a U.S. citizen provided you are otherwise eligible.
There are several requirements that citizenship candidates must meet - maintaining a primary U.S. residence, paying taxes, knowledge of U.S. history/civics and English, and showing good moral character during the five year (or three year, in marriage-based applications) period preceding the filing of paperwork.
What is good moral character? It's pretty much what it sounds like, though immigration law doesn't offer a precise definition. According to the U.S. Citizenship and Immigration Service (USCIS), good moral character "has been interpreted as meaning character which measures up to the standards of average citizens of the community in which the applicant resides, and thus does not necessarily require the highest degree of moral excellence. Good moral character has not been a static term since the standards of a community often change with the passage of time."
Someone who is convicted of a crime involving "moral turpitude" would have a difficult time meeting the good moral character requirement. Again, moral turpitude isn't exactly defined for immigration purposes, but you can gather what it means, more or less - crimes involving murder, rape, child abuse, drug dealing, tax evasion, fraud and many others.
A single DUI conviction isn't considered a crime of moral turpitude, and probably not a crime that goes against good moral character. (More than one conviction, of course, would be an entirely different story.)
As your conviction took place last year, your attorney might well advise you to wait until five years after the date of the conviction, because the naturalization application requires that the candidate show good moral character for the five year period prior to filing. If you received probation for the crime you couldn't be naturalized until this period ends.
Alcoholics Anonymous is by definition a private organization, and no one needs to know that you're a member. Your involvement with the organization will not have any bearing on your citizenship application - and good for you for addressing your problem.
Again, get yourself an attorney before doing anything. The same advice goes for anyone with a criminal record. USCIS regularly denies applications (and starts deportation proceedings) when the applicant finds himself on the wrong side of the law.