Background checks have become a staple of employment in many realms. If you have an indiscretion in your past, own it but give a detailed explanation about how you have remedied any likelihood of recurrence, via rehab, therapy, or other means. Let the interviewer know that this problem is no longer a concern but also state, as a gesture of good faith, that you are comfortable with a period of probation or supervision.
The right answer is 'No,' but you may have had a problem in your past for which you would have to answer, 'Yes.' If so, your job is to turn things around and make them comfortable with you. For the sake of example, below is a sample answer of someone with a substance abuse history:
