Best options that PCPartPicker are showing right now are the Athlon II X4 640 ($75 USD) & 645 ($95 USD) (https://pcpartpicker.com/products/cpu/#k=3&sort=price&page=1). Basically, they're Phenom II X4 940/945 chips with the L3 cache disabled. Tom's Hardware rates them as 4th-tier CPUs (http://www.tomshardware.com/reviews/cpu-hierarchy,4312.html), right behind the Phenom II X4 975/980 & X6 1090T/1100T chips. It's possible some other vendors might have something else available -- given the choice, I'd prefer a CPU with the L3 cache on it myself -- but you may not have a whole lot of selection out there.
As to getting a Socket AM3 CPU...
-- If you're doing this because your old CPU is busted, but everything else is working OK & you don't need newer hardware (i.e. playing much older games or using it primarily as a HTPC or for email/Internet surfing), then just getting a replacement Socket AM3 CPU makes a lot of sense.
-- If you're doing this because someone gave you the motherboard (& either the RAM & other parts, or you have them leftover from a prior build), then again, as long as this is for a secondary PC you should be fine.
-- If you're doing this because you plan on buying that Crosshair III motherboard, DON'T. You're better off going with something much newer -- heck, even an FX-8320-based system will outperform this one. If you just bought the motherboard, take it back pronto & get your money back.