It can't, however, be any old copper peptide. Look for something called GHK. This is the one that has the science backing it up. It isn't that easy to get though as the patents are closely held. One owner is Skin Biology. I have had great success with Folligen, Skin Biology's hair growth treatment, and Super Cop 2X.
Super Cop 2X is strong stuff though and there are plenty of people who report irritation and reactions. Oddly enough, given that I am the dermatological equivalent of the Princess and the Pea, I've never had a problem with it. Anyway, Skin Biology has brought out Super GHK Copper Peptide Serum ($39.95 for 15ml) for those that are sensitive and it can be used around the eye area (something I wouldn't dream of doing with Super Cop 2X). Nevertheless, it is still pretty potent and, according to Skin Biology, it has 50 times more copper peptide than typical GHK formulations.
Super GHK also has tripeptide 1, a relatively new anti-aging peptide, some vitamin E, allantoin (a soother) and aloe. I'd prefer it if it came without the parabens and diazolidinyl urea (preservatives), but otherwise this is well worth checking out.
By the way, I was intrigued to discover a source of pure GHK. Cellbone Technology sells GHK Copper Peptide solution for $36 for 25ml. It is recommended for use in concentrations of 10%. I must admit that I am sorely tempted. The notion of whipping up my own potions is becoming an increasingly seductive one.