There Are 2 Options If You Want To Continue Using Xbox Live With A Modchipped Xbox 360.
Option 1.
DVD Drive Firmware Flash
Pros
-Play games backed up onto dual layer DVD's
-Xbox Live safe*
Cons
-You still need to use discs.
-The latest games require 8.7gb of space (xgd3) and regular dual layer DVD's only has 8.5gb so 200mb needs to be overburned which only certain DVD burners can do.
-*Games need to be copied correctly to be Xbox Live safe which can be a bit of a process.
-A special drive is required to read your original game discs to your computer.
See here for more information if you have a Phat Xbox 360
See here for more information if you have a Slim Xbox 360
Option 2.
Reset Glitch Hack With Dual Nand
Pros
-Like having 2 Xbox's in one.
-Easily change between hacked mode and stock mode.
-Play games off your hard drive with out the disc in hacked mode.
-Install and run homebrew applications in hacked mode.
-Mod/Hack games
-Xbox Live safe in stock mode.
Cons
-Games cannot be played off your hard drive with out the disc in stock mode.
-Homebrew will not work in stock mode.