Here's what I recieved from LucasArts tech support when I emailed them about the problem:
1. You may need to go into the Xbox settings/clock section and check the TIME and DATE. Is it correct? If not, please change it to the proper TIME and DATE.
2. Try clearing your cache of the game. To clear your Xbox's cache of [KOTOR], you need at least three other Xbox games. Place the first game in and let it load until it gets to the game's main menu. Next, repeat this process with the other two games. Once finished, place in [KOTOR] and then try the game.
Microsoft's tech support suggested a similar solution:
Clean the disc:
1. Hold disc by the edges without touching the surface with your fingers.
2. Clean the disc with a soft cloth, lightly wiping from the center outwards.
3. Do not use solvents or chemicals to clean the disc.
4. Check the disc for any obvious signs of damage.
5. Try to play the game again.
If this does not work, you can try to clear the game cache on the hard disk. First, if you have a memory unit available, copy all of the games for this title that you have saved to the hard drive to a memory unit:
1. Insert a memory unit into a controller connected to your Xbox console.
2. Open the DVD tray and remove the DVD disk, if present.
3. Close the DVD tray and re-start your Xbox console.
4. Choose the "Memory" option from the Dashboard.
5. Choose the "Xbox Hard Disk".
6. Locate the game you wish to back up in the list of games.
7. Once you have selected the game, choose the appropriate save game icon (Save game icons are located to the right of the game icon. Each save game is identified with a name, date, time, and size).
8. Press A to bring up the Copy/Delete menu for the save game. (NOTE: If Copy is not available, then you have not chosen a save game file).
9. Choose Save.
10. Press A again to save to the appropriate Memory Unit.
11. Once the copy is complete, press B to return to the list of save games.
12. Repeat these steps as necessary to backup your other save games for this title.
Then, delete the icon of this game title from the list of games:
1. Select the large game icon to the left of the list and press A.
2. Press A again to delete the game cache file. (NOTE: Delete should be the only available choice. If Copy is present then you have chosen a game save file and not the game cache file. Press B to return to the list and choose the leftmost icon).
3. Select Yes to permanently delete the game cache.
4. Confirm that the icon is no longer listed and re-start your Xbox console.
5. Insert the game disc and either load your latest saved game from the memory unit, or play the game from the beginning.
If the above troubleshooting does not resolve the issue, the disc may be defective. Try exchanging it at the place of purchase. If this has already been done, it may be a hardware issue that requires repair.
I ended up having to return the game and getting another copy