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,
--Phil