The fob you have has a different FCC code than the system in the vehicle. They aren't unique to a single vehicle but for some reason manufacturers use different one's in different situations. Search the forum or post to see what others have for theirs. A Google search might even get you what you need. You could check out e-bay for replacement fobs for your vehicle, but if more than 1 code was used you can't be sure what you'll get. Most of the time you'll find the FCC code listed in the details of the auction listing. Once you have the right fob, it should be as simple as following the programming instructions that you can find easily - and they usually are included with the replacement.
Item model number FCC ID: LHJ011
Manufacturer Part Number 21997127, 15186200 Memory #1, 15186201 Memory #2, 15132197 Memory #1, 15132198 Memory #2, 10377295, 22730827, 15186203
Just found this on an amazon listed item with a Google Search for "2003 Tahoe replacement fob" if the fob you have has the same FCC ID it should work, unless there are other ID's that were used