NOTE – This method no longer works, please see the new article here.
Some people have avoided getting a Chromebook purely because Skype isn’t available. However, there is a way to get this working, and when you’ve completed one of these three steps the end product is very good indeed. The solution involves running the Android version of the app on your Chromebook. Google have so far announced four Android apps for the Chromebook recently but that’s kinda where things have stopped. There’s three ways to get Skype working. The first way is slightly more complex than the other methods, but hey – we’re hardcore. For the majority, the second method is the fastest. 
The first method involves a certain amount of “faff” and you’ll need a Linux server, which I appreciate not everyone has. To begin with you’ll need to get one of the official Android-based apps for your Chromebook. I installed Kids Sight Words because, well… it was just the one I clicked on. This installs the required “bits” that you’re going to need to add your own Android APK. The next bit involves a Linux server. You might not have one of these kicking around to be honest. You can buy / rent a virtual machine for not-that-much, especially if it’s a low-powered one (do a search for “cheap VPS” and find one if you want to get into this a bit more). You’ll then need to install some stuff.. 1 – Install nodejs. I grabbed the installer here. 2 – Install npm. I basically just ran this command on a CentOS box..
curl -L https://npmjs.org/install.sh | sh
3 – Install the ChromeOS-APK tool by typing..
npm install chromeos-apk -g
Once you’ve got all that you can grab yourself an APK and convert it. To do this you’ll need to get onto your Linux server and “locate” the APK you need. As you may know, there’s plenty of APKs kicking around the internet. Some savoury. Some unsavoury. Finding the right APK is a tricky business, and if you “stumble across” one on the internet it could have things lurking in it that you might not want. Perhaps the best way to get the APK you require is to grab an Android app called APK Downloader. You then just search the Google Play store as normal and it’ll download the APK file to your phone. 
Once you’ve got the APK, do a “wget” to get or SCP the file to your Linux box you can then do this command to convert the Android APK to a ChromeOS APK..
chromeos-apk /path/to/yourapp.apk –tablet
You don’t need to put “–tablet” at the end, but it does fill the screen better on your Chromebook if you do that. You then need to put the resulting files onto your Chromebook. Next, go into your Chromebook, go to Tools->Extensions and Enable Developer Mode. Hit “Load Unpacked Extension” and open the folder containing the files you created. I got an error when I tried Skype, but it seemed to work and the test calls I made worked absolutely fine. Apologies in advance for the slightly iffy video below (filmed in the garage if you’re wondering), but this hopefully shows you just how smooth the app is. It really does feel and operate like a native app… http://youtu.be/-cQkJGpvLqs OK. There’s a lot of stuff there isn’t there? A lot of hoops to jump through. Luckily there’s a second and easier way to achieve all this. You can skip a lot of the steps and just head to skypeforchromebook.cf, which seems to have the file in a handy zip format. They’ve also now added the smartphone version at the bottom of their page, so if you find yourself struggling to navigate the tablet version (like I did in the video above), simply download that one instead. You then just need to download the ZIP file, open it up in Chrome and point your Unpacked Extension loader to the main folder (com.Skype.raider). Boom. You’re using Skype on your Chromebook baby, and it works an absolute treat. Here’s the ZIP file downloaded and opened.. Then I just click “Load unpacked extension”.. That’s all there is to it. You’ll get a shortcut to the app in the usual place and you can go ahead and launch the app from the extensions screen.. Oh, by the way. All the usual warnings go with this. I can’t vouch for that particular Skype file and please don’t blame me if this molested Android APK makes your Chromebook implode. All I can say is that it worked OK on mine. Hopefully before long Android developers can just flick a switch and make their apps available on Chromebooks too, then there won’t be quite so much faff. 
The third method is probably the easiest if you want further Android appsb installed. Twerk is a Chrome app for packaging Android apps and seems to work rather well. It’s still “in development” and you may need to tweak a few settings.