Instructions
Power on your Xbox game console. When the system loads, go to "My Xbox."
Navigate through the Xbox dashboard and select the "Memory" menu.
Navigate to the "Hard Drive" menu and select the "Gamer Profiles" sub-menu.
Find the profile you no longer want and press "A" to pull up two options, "Move" and "Delete." Highlight and select "Delete" by pressing "A." You will see a message asking you to confirm that you really want to delete the profile. Do so and the profile and its attached gamertag will be deleted from your system.