Tow package? Trailer brakes!
My Tahoe 1500 with tow package (3.73 gears, transmission cooler and load distributing hitch) is rated at 7700 Lbs, so if your rig is rated the same, you're within the tow limits, though closing in on the max.
If yours is a K-1500 4WD (from my 2004 owners' manual) if you have the 5300 V8 3.73 gears your capacity is 7,500 lbs. (3 401 kg), if you have the 4.10 gears it's 7,800 lbs. (3 538 kg)
Check your owners' manual for your truck specifics.
I would also suggest you get trailer brakes (electric controller in your truck) on something that heavy (if you haven't thought of that already) .
Joe