Sign up here and you can download the ownsers manual in PDF format and it will give you a matrix of towingcapacity by chassis/engine/gears for that year.
https://www.mygmlink.com/main/US/en/chevrolet/home
(Free)
Here is GMCanada link to figure out capacity.
http://www.gmcanada.com/english/truckguide/pick_trail_capacity.html
I don't know on tahoe, but should be within capacity of a 1/2 ton pickup. If it doesn't have a tranny cooler I would add one. I assume you will be using a weight distributing hitch also, that I believe is necessary.
This is from an '01 pickup manual:
C-1500 Regular Cab Short Box (2WD)*
Engine (Trans.) Axle
Ratio
Max. Trailer Wt.
4300 V6 (Auto) 3.08 4,700 lbs. (2 132 kg)
3.42 5,200 lbs. (2 359 kg)
4300 V6 (Manual) 3.08 3,700 lbs. (1 678 kg)
3.42 4,200 lbs. (1 905 kg)
4800 V8 (Auto) 3.42 6,600 lbs. (2 994 kg)
3.73 7,600 lbs. (3 447 kg)
4800 V8 (Manual) 3.42 4,600 lbs. (2 087 kg)
3.73 5,600 lbs. (2 540 kg)
5300 V8 3.42 7,600 lbs. (3 447 kg)
3.73 8,600 lbs. (3 901 kg)
C-1500 Extended Cab Short Box (2WD)*
Engine (Trans.) Axle
Ratio
Max. Trailer Wt.
4300 V6 (Auto) 3.42 4,900 lbs. (2 223 kg)
3.73 5,900 lbs. (2 676 kg)
4300 V6 (Manual) 3.42 3,900 lbs. (1 769 kg)
4800 V8 (Auto) 3.42 6,300 lbs. (2 858 kg)
3.73 7,300 lbs. (3 311 kg)
4800 V8 (Manual) 3.42 4,300 lbs. (1 950 kg)
3.73 5,300 lbs. (2 404 kg)
5300 V8 3.42 7,300 lbs. (3 311 kg)
3.73 8,300 lbs. (3 765 kg)
C-1500 Extended Cab Long Box (2WD)*
Engine (Trans.) Axle
Ratio
Max. Trailer Wt.
4800 V8 (Auto) 3.42 6,100 lbs. (2 767 kg)
3.73 7,100 lbs. (3 220 kg)
4800 V8 (Manual) 3.42 4,100 lbs. (1 860 kg)
3.73 5,100 lbs. (2 313 kg)
5300 V8 3.42 7,100 lbs. (3 220 kg)
3.73 8,100 lbs. (3 674 kg)
C-1500 Regular Cab Long Box (2WD)*
Engine (Trans.) Axle
Ratio
Max. Trailer Wt.
4300 V6 (Auto) 3.08 4,600 lbs. (2 087 kg)
3.42 5,100 lbs. (2 313 kg)
4300 V6 (Manual) 3.08 3,600 lbs. (1 633 kg)
3.42 4,100 lbs. (1 860 kg)
4800 V8 (Auto) 3.42 6,500 lbs. (2 948 kg)
3.73 7,500 lbs. (3 402 kg)
4800 V8 (Manual) 3.42 4,500 lbs. (2 041 kg)
3.73 5,500 lbs. (2 495 kg)
5300 V8 3.42 7,500 lbs. (3 402 kg)
3.73 8,500 lbs. (3 856 kg)
K-1500 Regular Cab Short Box (4WD)*
Engine (Trans.) Axle
Ratio
Max. Trailer Wt.
4300 V6 (Auto) 3.42 4,900 lbs. (2 223 kg)
3.73 5,400 lbs. (2 449 kg)
4300 V6 (Manual) 3.42 3,900 lbs. (1 769 kg)
3.73 4,400 lbs. (1 996 kg)
4800 V8 (Auto) 3.73 7,300 lbs. (3 311 kg)
4.10 8,300 lbs. (3 765 kg)
4800 V8 (Manual) 3.73 5,300 lbs. (2 404 kg)
4.10 6,300 lbs. (2 858 kg)
5300 V8 3.73 8,300 lbs. (3 765 kg)
4.10 9,300 lbs. (4 218 kg)
K-1500 Extended Cab Short Box (4WD)*
Engine (Trans.) Axle
Ratio
Max. Trailer Wt.
4800 V8 (Auto) 3.73 7,000 lbs. (3 175 kg)
4.10 8,000 lbs. (3 629 kg)
4800 V8 (Manual) 3.73 5,000 lbs. (2 268 kg)
4.10 6,000 lbs. (2 624 kg)
5300 V8 3.73 8,000 lbs. (3 629 kg)
4.10 9,000 lbs. (4 082 kg)
K-1500 Regular Cab Long Box (4WD)*
Engine (Trans.) Axle
Ratio
Max. Trailer Wt.
4300 V6 (Auto) 3.42 4,800 lbs. (2 177 kg)
3.73 5,300 lbs. (2 404 kg)
4300 V6 (Manual) 3.42 3,800 lbs. (1 724 kg)
3.73 4,300 lbs. (1 950 kg)
4800 V8 (Auto) 3.73 7,200 lbs. (3 266 kg)
4.10 8,200 lbs. (3 719 kg)
4800 V8 (Manual) 3.73 5,200 lbs. (2 359 kg)
4.10 6,200 lbs. (2 812 kg)
5300 V8 3.73 8,200 lbs. (3 719 kg)
4.10 9,200 lbs. (4 173 kg)
K-1500 Extended Cab Long Box (4WD)*
Engine (Trans.) Axle
Ratio
Max. Trailer Wt.
4800 V8 (Auto) 3.73 6,800 lbs. (3 084 kg)
4.10 7,800 lbs. (3 538 kg)
4800 V8 (Manual) 3.73 4,800 lbs. (2 177 kg)
4.10 5,800 lbs. (2 631 kg)
5300 V8 3.73 7,800 lbs. (3 538 kg)
4.10 8,800 lbs. (3 992 kg)