Falco can chaingrab (to some extent) every noteworthy character. I think the one exception is Marth, and I'm not sure if the Pillar works on marth or not. Marth still gets boned by running usmash after a dthrow though. Plus they have to upb to avoid the changrab and Falco has a great punish game. Just don't let him take you to Lylat or Battlefield (on the neutrals).
Actually Falco gets two dthrows and a spike on Marth from 0%, but that's it. Pillaring doesn't work, and Marth can Fair/upB you before you can run in and Usmash. Unless you're at the ledge, running forward and shielding to bait the upB is probably your best bet.
Other than that, he chains on MK, Snake, Falco, DDD, GW, Diddy, Wario, Lucario (is it 3? I saw Zex chain three, then pillar twice, then usmash for a 0-70% on several lucarios at UCD Monthlies 2), Pikachu, DK, Ice Climbers (granted the other can break it out), ZSS, TL, Pit, Wolf, Luigi gets out with nair, Bowser, Fox (that one is really weird), Sheik, Ike, Mario, Lucas, Ness, PT (all characters with varrying effectiveness), Link, Ganondorf, and Captain Falcon.
Lucario should be able to utilt you after the dair but before you regrab when you try to pillar. DON'T TRY TO CG THE IC'S. They can break out and, worst case scenario, you'll get grabbed by them. Not pretty. ZSS can break out with downB. Fox is unspikable after the CG unless he's on the stage (or DIs wrong).
For the most part (Jiggz is the only exception that comes to mind) if you can't chaingrab them you can pillar them.
Don't think you'll get very farr pillaring Jiggz.