Between State Farm and Chase you should be in for a hassle free experience. Just make sure you handle everything promptly -- the credit card insurance usually has timelines you have to follow.

I had a hit and run drunk driver smash my parked Hertz rental. That's when I found out that State Farm has pre-negotiated everything with Hertz in exchange for their insurance replacement business. So no loss of use fees and other types of gouges rental car companies are notorious for.

I gave my info to Hertz, and filled out a form with Amex. State Farm handled everything with Hertz, and the deductible covered by Amex, so I assume the same with Chase.

The only effort more on my part was to fax my State Farm declarations page to Amex. Other than that I had very little to do and everything was just taken care of.