In the trailer with Chief, we see, in the first shot of his HUD, a friendly marker. This is obviously Locke (Who else could it be? Arbiter?). Maybe the two teamed up. Locke would have offered to help him, but planned on betraying him. When he did, Chief went after him. Maybe these trailers are in chronological order. In Locke’s trailer, the statue of Chief is in good condition, and he probably just turned on Chief. Maybe Arbiter stopped him, and Chief got away. There was some other stuff that went down, and Chief recovered, but they had another showdown in the same spot, doing damage to the statue. Finally, Chief tells Locke that his mission has been completed. BOOM. He may let him live or something, though, or something goes down that lets Locke escape. Then, Halo 2-style, the game ends.
Edit: In addition, Locke’s scene is during the day and Chief’s scene is in the evening, so there’s more evidence for my theory.