Angel Face is a handsome, very blond young man who joins first Fight Club, then Project Mayhem. The Narrator is quite resentful of him, for Angel Face represents a replacement for him. Tyler shows affection towards Angel Face during Project Mayhem, while the Narrator wasn't even aware that the project was occurring at all. This directly leads to the Narrator's nearly killing Angel Face in a fight. Angel Face later tries to take charge in Tyler's absence when Bob is killed. He is Tyler's ideal solider, better than the Narrator; therefore, the Narrator hates him.
Mike writes, "I just thought I'd let you know that the angelic face guy appears in a another scene in the movie. In the scene where the narrator is talking about Tyler's movie projectionist job, it shows a few peices of the porno film as Tyler works on them, if you pause the movie, you can see the blond angelic face guy having sex on a piece of the film."
Here is the film frame in question (enlarged with the offensive bits cropped out-- I do have SOME shame, you know). Sure enough, it's Angel Face. No one else could be that blond.