Skype is not just used for audio or video chat, but for plain old text chatting too. I use Skype with a Outlook.com account on Ubuntu. I wish I could just chat from inside Outlook.com, like you can use GChat from inside Gmail web interface. There are Skype for Outlook.com extensions available for the major browsers, but they seem to install only on Windows. I could not install them on Linux. I wish this worked because it would be convenient to chat with Skype contacts directly from my Outlook.com webpage messaging sidebar.
Instead, I use the Skype client which is available for various Linux distributions. Just download that for your distribution here and install it. For Ubuntu, this downloads a multiarch
.deb file. The recent versions of Skype client allow you to use your Outlook.com account. Just choose the Microsoft account option during login.
Tried with: Skype 4.2 for Linux and Ubuntu 12.04