Microsoft has posted updates for Windows 8.1 (x86/x84) and Windows Server 2012 R2 to prevent Skype from crashing.

According to the associated KB article, Skype Windows Store app crashes in Windows 8.1 and in Windows Server 2012 R2, this will fix an issue when you start the Skype Windows Store app in Windows 8.1 or in Windows Server 2012 R2 and the app immediately crashes and Windows returns to the Start screen.

This update will be available in Windows Update but you can download the appropriate version for your Windows 8.1 device by using the links above.