All Mobile Solution: 12/16/12

Pre-requisite
a) This root package is compatible only with Galaxy S3 running on Android v4.1.1 XXDLIH, therefore do not try this rooting on any other variants.
b) Ensure that USB Drivers are installed for Galaxy S3 and also enable the USB debugging mode.
c) Back up all important data before proceeding.
d) The battery of Galaxy S3 should be charged above 80 per cent. See here how to check the battery percentage.

Steps to Root Android 4.1.1 XXDLIH on Galaxy S3
1) Download CF-Root-SGS3-v6.4.zip for Galaxy S3 to the computer
2) Download Odin v1.85
3) Power off Galaxy S3 and place it into Download Mode. To do so turn on the phone while pressing Volume Down and Home button together
4) Ensure that USB Drivers are installed on the computer
5) Open Odin on computer. Connect the Galaxy S3 to the computer while the phone is in download mode
6) One of the ID:COM boxes can be seen turning yellow with the COM port number if the phone is connected to the computer successfully
7) Select the root package, CF-Root-SGS3-v6.4.zip, which has been extracted in step-1
8) Select start button in ODIN to begin installation which will take a few minutes
9) Upon completion of installation process, the phone will restart
10) Once the home screen is seen the phone may safely be unplugged from the computer. Switch off the phone once again. Enter recovery mode by turning on the phone while pressing Volume Up, Home and Power buttons together
11) In the recovery menu select wipe data/factory reset
12) Select reboot system now to boot the device
Samsung Galaxy S3 running on Android 4.1.1 XXDLIH Jelly Bean official firmware is now rooted successfully.