offer letter before or after background check?

About a week and a half ago I was offered a job at the interview. Later that day, I got an e-mail congratulating me, giving me a start date, and detailing that I would receive an offer letter in a few days, a background check and once that clears, my start up paperwork.

As I stated, it's been a week and a half and I've only just gotten the background check two days ago, which is still processing. The e-mail made it sound like the offer letter would come first, but be conditional on the background check. Should I reach out to the company and ask where it is? Or wait until the background check passes? I ask because the initial e-mail asked for the offer letter to be returned as soon as possible, but it's about a week late.