if what you have there now is chiping easy, then no matter what you put on top of it it'll still be no good because the underlying paint will still have the adhesion problem to begin with. if it's chipping & your seeing chrome undernieth then you will have to strip it. depending how much material you built up already agressive sanding may be your best bet. if that gets hopeless because of a lot of material buildup then there is a paint stripper you can use. just about any auto body paint supply house should have it. you'll be looking for an "aerosol urethane bumper stripper" this won't hurt the plastic but it can make a mess in other ways, again, depending on how much material you have on there. if you have a lot then it may not strip it all & you'll still have a ton of sanding, but it'll soften up the paint to the point that you can just about wipe it off for the most part... it's the corners & crevices that give the most problem with having to sand what the stripper doesn't remove.
the stripper is safe for plastic but it is still very caustic so wear gloves if you have sensitive skin or at least flush with water soon after handling, don't spray where the wind can take the overspray & like coat the side of the fx either

I would only use this if the sanding got to be too much though...