Halo: Reach has been optimized to run from your Xbox 360’s Hard Drive. If you install Halo: Reach to your Xbox 360’s Hard Drive you will notice significantly faster loading speeds throughout the game. Here's how to make the magic happen:
Load the Xbox LIVE Dashboard and navigate to the My Xbox tile with Halo: Reach in the disc tray.
Press Y to bring up the game options screen and select "Install Game" from the menu.
Wait for it...
Bam. You did it!
Select "Play Game" and enjoy Halo: Reach with faster loading times. Thanks for playing!