Remote Debugging for Chrome iOS (and Safari)

Question

With the recent release of Chrome for iOS, I was wondering how do you enable remote debugging for Chrome iOS?

Update: With the release of iOS 6, remote debugging can now be done with Safari.

Answer 1

Update:

This is not the best answer anymore, please follow gregers' advice.

New answer:

Use Weinre.

Old answer:

You can now use Safari for remote debugging. But it requires iOS 6.

Here is a quick translation of http://html5-mobile.de/blog/ios6-remote-debugging-web-inspector

1. Connect your iDevice via USB with your Mac
2. Open Safari on your Mac and activate the dev tools
3. On your iDevice: go to settings > safari > advanced and activate the web inspector
4. Go to any website with your iDevice
5. On your Mac: Open the developer menu and chose the site from your iDevice (its at the top Safari Menu)

As pointed out by Simons answer one need to turn off private browsing to make remote debugging work.

Settings > Safari > Private Browsing > OFF