I would NOT do this, especially not until you're off probation. Probation still lasts for a year, right? I'm sure some of the chiefs are "cool," but some definitely are not.

Unless you have a previous personal relationship with that particular chief, and can trust them, I would not trust a chief.

I consider talking to a chief like talking to the police. Anything you say or do can be used against you.

If you feel the need to communicate your concerns to the company, I'd relay via my SWAPA rep.