***CONFIRMED 100% WORKING ON AT&T CAPTIVATE BY MOOSEFIST***
The following method should be relatively care-free but there is always a risk with activities like rooting a device or flashing a new firmware.
1. Download
http://dl.dropbox.com/u/178498/SGH-I897%20Root%20Update.zip and rename to: update.zip
( «ammar»- I just added a new working link. I am not completely sure this is the right .zip I got the link from here http://www.attdroids.com/forum/samsung-Captivate-hacking/1138-Captivate-root.html . Please be careful. Onlly do this at your own risk.)2. On your device, navigate to Settings > Applications > USB settings and select Mass storage
3. Plug your device into your computer, select mount USB from your device's pull-down window
4. Copy the update.zip to the INTERNAL SD memory (~14gb on this drive, not the one w/ Avatar if you've still got the 2gb SD card in)
5. Turn your phone off.
6. Hold down volume up and volume down while powering on the phone, this should get you to a recovery menu, you may have to try this a few times.
7. In Recovery menu select 'Reinstall Packages' (use vol_down then power to select)
Phone will reboot and you have:
1. su+Superuser
2. busybox (/system/xbin/busybox)
Original credit goes to LeshaK at Samdroid
