You can program the remote portion of your 2003, 2004, and 2005 Hummer H1 remote yourself at home with these simple instructions.
There is also a free programming tutorial video below to show you how easy it is done.

IMPORTANT: Before entering programming mode, have in possession all of the transmitters you will be using on the vehicle. Once you program the transmitter, all previous codes will be erased from the memory. The other transmitters will not be functional until you program the transmitters again.
1. Close all vehicle doors.
2. Insert the key into the ignition.
3. Hold down the power UNLOCK button on the driver’s door panel-continue to hold down until instructed to release.
4. Perform steps 5 through 8 in fairly rapid succession.
5. Turn the ignition switch to the ON position (as far as you can go without starting the engine).
6. Turn the ignition switch to the OFF position.
7. Turn the ignition switch to the ON position.
8. Turn the ignition switch to the OFF position.
9. Release the power unlock button on the door panel. The vehicle will lock and unlock the doors automatically.
10. Hold down the LOCK and UNLOCK buttons on the transmitter simultaneously until the door locks and unlocks. This step may take up to 30 seconds.
11. Repeat the previous step (JUST THE LAST STEP) for each additional transmitter (including any existing transmitters).
12. Turn the ignition switch to the ON position in order to exit the transmitter programming mode.