"Paul" is a designer-machinist-rider in Chico, CA, who makes useful, clever, simple, wonderful bike parts—sometimes unique, sometimes his own take on existing parts.
His last name is Price, not Melvin. Melvin's what he named this chain tensioner. I looks like a derailer, but it doesn't shift. It just takes up chain slack (it's a chain tensioner), so it lets you ride a single-speed freewheel on a bike with vertical dropouts. Will has one of these on his bike.
(Horizontal dropouts let you slide the rear wheel back and forth to tension the chain.)
The beauty of using a tensioner is you aren't limited to just one gear. The Melvin wraps 20 teeth of chain, so you can have a single cog in back and even a 44/34/24 triple in front, although most people will use this with a double, probably a 40/26 or 38/24.
Single speed purists may turn their noses up at it, but if you have a rough and tumble bike and you ride trails and road, having a tensioner and a double or triple in front is better. It still feels like a single speed; there's no noise, the chain doesn't bounce at all and it's still harder than having a geared bike, but you can climb to the top of the mountain with your geared buddies instead of relegating your one speed bike to city-duty only.
Shimano makes a less expensive version, the Alfine tensioner. They both work great. Shimano won't notice if you buy theirs; Paul knows when you buy his, because we reorder. One more thing: You can adjust a rear derailer to stay in place and do the same.
Don't use this or the Shimano Alfine or any other chain tensioner on a fixed cog (no coasting). The wheel will lock up dangerously. Only on freewheels.
TIP FROM WILL:
Use a front derailleur or just shift it with your keys when you're taking a break at the crest of the hill. Push the tensioner forward so the chain is slack while you finger-shift off the bike. Shifting down with your foot while riding is easier than you'd imagine. Foot shifting up is difficult but do-able, especially if you have long chainstays.
There are plenty of cheaper tensioners out there that'll do the job, although I don't think there are many that wrap this much chain, but I suspect that people converting their bikes to two speeds would be more inclined to keep it that way if they use this gem of a tensioner made by Paul Components in Chico CA.
Set it up with the arm almost all the way extended when you're in the big cog in front so when you shift down it'll still be taut. It has spacers on the mounting bolt you can move around to get the chainline you want, and if you use a GearClamp you can leave it how it comes.
** Note **
We do not stock Paul parts on our shelf. We order them as they're ordered. The Paul Components factory in Chico is close by so we usually are able to get Paul parts orders out the same week. So, these parts are not available for same day in store pick-ups or expedited shipping orders.