GM issued a Technical Service Bulletin (TSB #06-03-09-004G) which may address squeaking noises coming from the rear suspension of the 2007-2010 H3 and H3T.
The squeaking is likely the result of debris getting lodged in between the rear leaf springs or a broken retaining clip.
If you’ve had this problem ask your local dealership about TSB #06-03-09-004G. Dealerships have been told to clean and lubricate the leaf springs and, if neccessary, replace the busted clip. All the work is covered under Hummer’s new car warranty, just make sure to check for age or mileage restrictions.