The twin brother of Samsung Galaxy S finally has a Gingerbread 2.3.5 update. With this update also comes a new method of rooting your Galaxy SL. This rooting guide is only for the Galaxy SL I9003 with 2.3.5 xxkpm firmware.

To check your firmware, go to your homescreen then tap Menu > Settings >About Phone and you should then see the Firmware Version. If you have the correct firmware version, then we’re ready to root your GALAXY SL.

Requirements:

• Samsung Galaxy SL I9003
• USB Data Cable
• Computer

1. First, download this file: GalaxySL_I9003_XXKP_rooting_2.3.5
2. Then, extract it to a new folder via Winzip/Winrar.
3. Open the new folder then double-click odin3_v1.0.exe
   
4. Next, turn off your phone.
5. Now enter download mode by pressing  down on Volume Down Key + OK button. While holding both simultaneously, press the Power Button. You should see this screen next: 
6. Connect your phone to your computer via USB Data Cable.
7. The Odin program will recognize your phone and you will see that the ID : COM section will turn yellow, which will mean that all the drivers have been successfully installed. 
8. Next, click the PDA tab and search for the CF-ROOT-XXKPM-20.10.2011.tar file you extracted earlier
9. Then click the START button. Now the rooting process will begin.
10. When finished, your phone should restart by itself. Restart it manually if it doesn’t.
11. After that, your phone is finally rooted. Congratulations!

Note: To make sure that there will be no problem with your phone after rooting, go into recovery mode and follow the steps below:

1. First, turn off your phone.
2. Next, turn it on by long pressing Volume Up + Menu, then press the Power button. The phone should now go into recovery mode.
3. In recovery mode, select Wipe data/factory reset. You also need to select wipe cache partition.
4. After that, go back and select reboot system now to restart your phone.

Now your phone should be free from errors like force close, etc.

Resources:

XDA Developers Forum