Earlier I'd posted instructions for installing the Linux Skype on Crouton on a Chromebook. That method works, but I'm happy to report there's a new method running Skype on ChromeOS itself (sort of).
It's not an official ChromeOS port of Skype, but the Android version of Skype repackaged for ChromeOS.
There's indications that Google will sooner-or-later start supporting Android applications on ChromeOS. Think of this as a preview of what the ChromeOS/Android future will be like.
The basic process is:
- Install Evernote
- Install Twerk
- Get the Skype APK file
- Drag the APK file into Twerk
- Pick a few settings
- Save as an unpacked Extension
- Load unpacked Extension
The first step, installing Evernote, has a side effect of installing a necessary component. I believe the Evernote app is an Android app packaged for ChromeOS. The next step, Twerk, is in the Chrome app store and it takes care of repackaging Android app's for ChromeOS.
All the details are on another dude's blog: http://www.head4space.com/install-skype-chromebook/