Originally Posted by mihlbach

If it is indeed a freewheel hub, not a freehub, you can take off the freewheel and install a fixed cog on the same threads via the rotafix method (without a lockring)...http://www.youtube.com/watch?v=5qIVEpyelP0
I wouldn't recommend this for a brakeless bike, because its remotely possible that the cog will come loose if you backpedal hard enough and/or don't tighten the cog enough. This is known as a suicide hub, but as long as the two brakes on the bike are functional you will still have the means to stop, so not a big deal. You can use red loctite for added security, but its not really necessary.
Is the rear hub is a freehub (i.e. the freewheel mechanism is in the hub itself), you will need a new wheel.



Can you post a close up of the hub?