All PS3s can play PSOne games. Make sure it's an official disc and not a copy. Copies won't play. Wikipedia says PS3s honor the region coding on PS2 and PSOne games though. You may not be able to play that title if it doesn't match the region on your PS3.
I thought it's only on the old fat PS3s. hmmm...
All PlayStation®3 video game consoles can play PlayStation® or "PSOne" video games.
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