It seems that Splinter Cell: Conviction has been having some problems with freezing early in the game on the Xbox 360. This is supposedly to do with the latest dashboard update, which is causing the game to freeze inexplicably around the second level of the game.
Ubisoft has posted a temporary fix for those having issues at the moment. The steps for fixing this problem temporarily involves disconnecting from Xbox Live and clearing system cache. The post on how to perform this fix reads:
Load to the Xbox 360 dashboard
Choose "System Settings"
Highlight your hard drive
Press "y" for device options
- from here just choose to clear system cache
"Sorry for the issue (for those running into it) and hold tight for further information."
Ubisoft is currently working to patch this problem so users will be able to continue play of the single player campaign of the game. Hopefully this is a quick fix and doesn't ruin anyone's time with the game.