I've not rented a car in Chetumal, and I'm told rentals are hard to find in that town, but Avis has, or did have, a location at the Hotel Los Cocos. However, I don't see a Chet location listed for Avis. Probably one of the other hotels in Chetumal could help arrange a car rental. You might be better off renting in Cancun or Playa del Carmen where there are lots of tourists and lots of rental car places.
--Lan Sluder