This is the safest method on how to root your U.S Samsung Galaxy S3 AT&T SGH-I747, Canada Telus,Rogers and Bell SGH-I747 variants without messing up your phone in no time. Many users already screwed up their Galaxy S3 devices from rooting methods that results to missing the IMEI number after loading or installing a wrong root kernels/clockworkmod recovery.
The IMEI is a 15-digit number under your battery. dialing *#06# should display the same number under your battery. If you get a different number or something like 0 / 00, you have corrupted your IMEI. Your network identifies your phone by its IMEI. Once you lost it, your carrier network provider would not provide service to your device, even after getting a new sim card. So, beware about that from happening to your precious Galaxy S3.
The idea on this root method is by injecting a rooted system image on the original stock ROM or firmware officially released by Samsung. So, the best thing about it is that you can simply root your Samsung Galaxy S3 phone without tripping the binary flash counter.
This rooting method is likely just manually installing the original firmware to your phone by using of Odin downloader tool.
Rooting Quick Guide
Odin flasher - Odin3_v3.07
USB Driver - Samsung Android USB Driver
Download and Extract the stock_root69.tar from the .7z file from the link below
Use PC with Windows OS (Odin will not work on Mac and Linux OSX)
Make sure to fully recharge your battery
Use the original supplied USB cable for your Galaxy S3
1. Run Odin on your PC desktop
2. Boot the Galaxy S3 into download mode screen for Odin.
Turn it off, once completely shut down hold down the 'HOME' + 'VOLUME DOWN' buttons and press the 'POWER' button for about 2 seconds until a WARNING! Screen appears. Press the 'VOLUME UP' button to continue or enter Download Mode.
3. Connect the phone to PC via USB. Then make sure you can see as phone "Added" in Odin log box or highlight the COM:ID once the device is detected,
4. In Odin window, DO Not tick 'RE-Partition' only Tick 'Auto Reboot' and 'F. Reset Time' and nothing else.
5. Now load the root system image root69.stock_ATT_I747UCLG1.tar (for AT&T) on the PDA button.
7. Wait until the flashing finishes and the phone completely reboots.
Grab the correct root system image according to your phone carrier, posted by mrRobinson here: http://forum.xda-developers.com/showthread.php?t=1739426
You can read more about missing IMEI number incidents posted by zeesubalpha here http://forum.xda-developers.com/showthread.php?t=1753833