Can I tow this trailer with this Tahoe?

Mike, I have done tens of thousands of miles, at least 70K, while towing a very similar rig (26', 4300lbs dry) with a pair of Tahoes, and a Chevy pick-up with the same drivetrain. You have plenty of truck to get the job done. Contrary to what was said, you absolutely will know it's back there. The rear end gearing can make a huge difference. I went from on 5.3 rig with a 3.21 rear to another with a 3.73. Absolutely amazing performance change. That said, these were both the old 4 speed auto. trans, which IIRC was long gone when your Tahoe was built. As a minimum you need slip on mirrors, a good brake controller, and a decent hitch. I use a Prodigy controller, and a Reese Dual-Cam. I also found that a pair of air bags in the rear coils really helped to keep the truck from squatting, when hitched up. I used Air-lift brand, which were cheap, but I had two bag failures over a few years. The manufacturer was quick and responsive, in replacing them under warranty. Good luck. I have a big diesel motorhome now, and really miss the Tahoe and trailer!