I use Amex rather than Chase, however there was no issue at all with me renting in Croatia and driving to Bosnia and Montenegro. I asked at the Hertz counter if there were any issues or permits required and they said no problem. And there were no issues at all at any border crossings, etc.

My first rental was a Ford Focus and the second was a decent Hyundai (can't recall the model) which was a triple upgrade they said.