WP MU Theme - How to hide part of the theme when someone is logged in

I was wondering how to hide part of the theme Blogs MU when someone is logged in.

Here is a screen shot:

http://awesomescreenshot.com/09c1t7qw93

A different page same piece of theme:

http://awesomescreenshot.com/0231t7r1f7

Thanks in Advance!
W.