Belt Driven Bike

I loved my bike as a kid.  I took it apart and put it back together all the time.  I frequently lost my chain and had to put it back on and get my hands all greasy and gross.  That was fine by me but my mom would freak out if I touched anything.  Why not replace the chain with a belt?  It would be less dirty, less expensive to replace and you wouldn't get you pants stuck in the gears anymore.