As far as I know (from doing a quick search via Google), Skype chooses not to support any Blackberry/Research in Motion products. During the search, it seems to be a high unlikelihood of it ever being supported.
There are a couple of options that I know of to use Skype on the Blackberry Playbook. Option 1 - Browser-utilized
Apparently the site http://imo.im/
allows you to utilize skype on the playbook but there have been noted limitations within this option. Option 2 - Android version
Sideload an Android Version (Top Blackberry Playbook Apps | Good e-Reader Android App Market and Store - Playbook App Market and Store
) and try it there. I did test this on my blackberry playbook and it does work, however I do not have a skype account and was unable to test any of the features.
Best of luck,