is there a way to create a new group (automagically) every time a new user is registered?

The group would be for that "new user" ie; 1 og per user

This would help in the following situation.

The main web site with bla, bla data
registered user(s)
-> has personal information they "DO NOT" want to share
-> has personal information they "DO" want to share

I have previously used the nodeaccess module for this, but the power of OG gives the user ALOT more "stuff" to use.

Ideas? ? ? ?

Thanks in advance,

Tim "t4him" Moyers