Black is one of the hardest colors to match. Here's what you do, the perfect solution that never fails.
Go buy a new Epiphone Les Paul, take it directly from the store and put it in to a glass case. Never touch it from that point on, just look. Then take the other one with the chip and use that one to play.
Sorry, but to a point I'm somewhat serious. If you have intentions to play and instrument, you can't let yourself get worked up about chips and dings. Unless you're using it for a photo shoot or music video, don't worry about it.
Black really is a very difficult color to match, as well as matching refraction on thick acrylic or polywhatever Epiphone finishes. If you want to obscure a big white spot where black is missing, stick some black nail polish on it and call it done A deluxe touchup would probably involve a bit of CA to build up to the surrounding finish. Anything more than that I would say is overkill for an Epihone LP. For the repair you're describing, I would literally be charging more than it would cost to replace the guitar with a new one.