The PS3 Slim doesn't and won't have any kind of retrocompatibility with the past PlayStation consoles. You can Google that, I'm not in my comp so I don't have the links on-hand, but I own the fat, non-retrocompatible PS3, and always like to read everything about my console.
If you wanna play back the Chrono Series, do it on your PSX or PS2, the retrocompatibles PS3 emule the games, hence there's high possibility they won't load but after several times, or will surelly freeze/bug. Both of my best friends have the old models of the fat PS3, and it happens when they try to play most of games like that, and also, there are games that just won't load.
As I said before, and as a PS3 owner and user, don't get it if you just want to play other consoles games in it, plus it will be hard to find one of the first models.