The fastest I took someone through their private was 30 days. It could be done quicker, but it's not enough to eat; you need to digest, too.

You didn't state what type of aircraft your unit is flying or the nature of the flying (type, amount, etc), but unless you're doing a lot of flying and getting some broad experience, it may be a leap to go from zero time to chief pilot in a short period of time.

Good counsel above; talk to other LEO's who have taken the same path. It sounds like your chief pilot is willing to give you the time of day and some counsel; the more information you can get, the better.