Does anyone know where to find a place on the web to set up a small forum for discussions of a small group of people (4 to 5, ATM, but up to a dozen should be possible)? It should be organizable into different topics and threads (just like a real forum) and enable users to upload files and images, although I don't need lots of storage space for that.
Most importantly, it should be a "closed shop", not open to the public. Neither readable by outsiders (access should be password-protected) nor indexable by bots like Google's. The intended use is for a small workshop.
I don't have an own server to set this up, which would probably be best, so I need a hosted solution. Preferably free.

I looked at a lot of collaboration platforms (like Basecamp, Joyent), but none I found so far will let you organize messages by topics and threads like a real forum. Some include chat solutions (like 37signals' Campfire), but real-time chat is not what I'm looking for. Wikis (like pbWiki) can't be structured in the way I need.
There are sites that give you free forums (like freeforums.org or nabble.com), but the forums you can create there all seem to be open to the public.
Any pointers?