The first place to look would be a blown head gasket, or; a stuck thermostat, bad water pump, low water, bad fan (mechanical and or electric) - all of which could cause a blown head gasket.
I would start with a tune up
the cars belt will start to brack and the car will stop
Remember the number one problem with these cars is fuel pump related. Check your fuel pump pressure; your pump may be getting weak.
how long does it run before it cuts out? If it runs for about 5 or 10 minutes and won't start again until it is cold it could be the crankshaft position sensor. If it runs for a few minutes, sounds more like a ECT (engine coolant temp) sensor.
The 2006 Chevrolet Tahoe runs on regular unleaded.
The 2004 Chevrolet Tahoe runs on regular unleaded.
The 2001 Chevrolet Tahoe runs on regular unleaded.
The 2003 Chevrolet Tahoe runs on regular unleaded.
The 2002 Chevrolet Tahoe runs on regular unleaded.
The 2007 Chevrolet Tahoe runs on regular unleaded.
The 2005 Chevrolet Tahoe runs on regular unleaded.
The 2008 Chevrolet Tahoe runs on regular unleaded.