The very first scene in Fight Club is Tyler with a gun in Jack's mouth and asking "Any last words?" Based on what we learn about their relationship throughout the movie, this scene doesn't make any sense.
Tyler can't kill Jack because they're the same person, so we wouldn't expect him to be able to follow through. Tyler also consistently supports Jack and pushes him through things, in his own words, he fully intends to drag Jack "kicking and screaming" through this whole affair, not kill him.
Aside from leading up to the best joke in the entire film, I can't see much reason he'd have to put a gun in his mouth.