From ModMyi - Wiki

To follow this guide any further you must be running OS X on an Intel Mac. This guide is for those running 1.1.1 iPhones on the AT&T network. This does not require downgrading to 1.0.2 first. For this method we are using the tiff jailbreak method. The program we are using is iJailbreak originally for the iPod Touch but this version is specifically coded by cashflowlogic for the iPhone.

Step One: Verify You are Running a 1.1.1 Phone

Start up iTunes. As you can see the phone is running 1.1.1.

Please exit out of iTunes

Step Two: Quitting iTunes Helper

Open up activity monitor. It is found in the Utilities folder on your mac.

Find the iTunes Helper process and click Quit Process.

You will be asked if you are sure. Click Quit.

Step Three: Getting Ready

Download iJailbreak. Mirror. Extract the archive to your desktop. If you get an error while extracting try using BOMArchive Helper (pre installed on your mac) or Zipeg. Drag the extracted iJailbreak folder to the Applications folder on your computer. It will not work properly if it is not in the Applications folder.

Browse into the iJailbreak Folder.

Step Four: Going Through the Motions

At this point I would recommend you go to settings->general->autolock on your iPhone and choose to have it never lock. Run iJailbreak and click Jailbreak.

Press OK.

When prompted go to http://jailbreak.toc2rta.com/ via the Safari browser on your iPhone. Safari will crash and you'll be back to the homescreen. Press OK.

You will see the screen below for about 8 mins. Don't touch anything.

You'll be prompted to turn your iPhone off and then back on. When it has fully rebooted click OK.

You'll be prompted to turn your iPhone off and then back on. When it has fully rebooted click OK.

You'll be prompted to turn your iPhone off and then back on. When it has fully rebooted click OK.

When the program is finished it will go back the first screen.

Step Five: Congrats

Now you have a Jailbreaked 1.1.1 phone with Installer installed. You can run installer via the iPhones main menu. Happy modding.

In the snapshot after running the safari crash it says connect your phone, but it was connected all the time before and during the crash... someone needs correct it.