Captivate users, are you jealous of the slew of one-click root options for the DROID X, EVO 4G, and Incredible? No need to be, any longer, as a one-click root application has been developed for the AT&T Captivate. Note, the application only works with Windows. Sorry, Ubuntu and Mac users. And you will need Samsung's Captivate USB drivers and .NET Framework v4 installed (Vista and Win7 come with this pre-loaded).

Instructions (from XDA... hit the source link below for support):

1. Make sure your phone is on USB Debug mode: (MENU > Settings > Applications > Developement > USB debugging = Checked )

2. For Windows x86 and x64 systems make sure that the Samsung Drivers are installed. You can get them here.

3. Extract the contents of GalaxyS_Captivate_One-Click_Root.rar to a folder.

4. Connect your phone to your PC via the USB cable and launch the file "AT&T Captivate One-Click Root.exe" file.

5. Click the "One-Click Root" button. This will launch a command prompt follow the instructions in the CMD window.

Done! You are rooted.

Download One-Click Root program here
Download .Net Framework version 4 here

Note: This program only works with Android 2.1. Don't use this method once 2.2 starts rolling out!

Cheers to TGA_Gunnman and the rest of the folks at XDA!

Source: XDA