Will I be able to get a company car with a DUI on my record?

I was charged with a DUI in December of 2010. I pled guilty in June and completed all court ordered programs and paid all fines and costs. The night of the DUI there was a bad ice storm, causing someone to drive into my car. I called the police. They ended up breathalyzing me and taking me to jail for a small amount over my state’s .08 limit.

I recently signed an offer letter with a new company. I’ll be starting for them on Oct. 3. Part of the offer is a company car, as my job requires about 50% travel within my state.

Will this DUI prevent me from getting the company car and/or the job?