My guess would be that Use unique permissions instead of Use same
permissions as parent site  is in effect and you have to asssign users  to the
Project Workspace

It does not matter whether Use Unique or Use Same as Parent is
chosen. The person that created the site  is even getting the
authentication box. If he clicks cancel it allows him onto the site
but when he clicks on a link it then prompts  for authentication
again.

Just to check, it is a SharePoint authentication  box and not a proxy
authentication or some other type, correct?

Yes, it is an Sharepoint authentication  box not some other type.

Have you tried adding the site  to Trusted Sites in IE? You can try changing
the browser settings to 'Automatically logon using current username and
password'

Yes. The person can access the parent site  just fine and if he
creates a child site using a Team Site template  he has no problems.
Its just the Project Workspace template on that site collection  that
is the problem. We can create  Project Workspaces on other
collections and it does not prompt for authentication  from site
users.

Looks to me like a permissions problem back in your site  def’s or style sheets. If you’ve create  new images, Site Definitions or styles in the 60 hive, check to make sure the permissions are correct.

Users have Read & Execute permissions in the 60 hive and they are
propagated down.

Again, it is only on this one site  collection that there is a
problem. Users are not getting prompted  on Project Workspaces
created in other site collections that they are members of.