Dawn, the first campaign mission, picks up right after the ending of Halo 3. Cortana wakes the Chief as the ship is under attack; it isn't immediately clear what is attacking the ship, but she needs his help protecting it. This marks both the literal and figurative return of Master Chief, and that immediately comes across in the opening sequence. The Chief and Cortana reunite and he heads out to find out what's going on. Unfortunately, what they find isn't exactly comforting: they're right in the middle of a Covenant fleet in the orbit of a Forerunner planet, Requiem.
It wasn't all story reveals either though, as I was able to experience one of the coolest introductions for the Halo series in a while: first-person action sequences. Sure, technically the entire game is a first-person action sequence, but at one point the Chief must climb an elevator shaft while dodging falling metal. That might sound like a terribly generic game sequence, but it wasn't a quick-time event; I had full control the entire time. I even managed to run straight into a falling piece of metal, only to have the Chief fall before barely grabbing onto a ledge of the elevator shaft in time. It might be somewhat of a videogame cliche, but it's also an evolution of the classic Halo gameplay, something I don't think we would never see in the original trilogy, and that makes it noteworthy.
A good part of this level took place outside the ship in empty space, trying to fight off the Covenant and do other important space stuff in zero-gravity. It doesn't really matter what I was out there doing; what matters is that I felt like a badass the entire time. It didn't feel obnoxiously floaty either, presumably because the Chief's suit is heavy and somewhat magnetized, so he stuck to the ship and controlled very similarly to how he does in normal gravity. I ran out of ammunition while outside the ship, but thankfully there were plenty of weapons floating through space for me to grab.
After a certain amount of fighting, things turned bad real quick and we were sucked into the Forerunner planet. We weren't told what happens in the second chapter, but it's quite apparent that things aren't going well for the Chief and Cortana when they crash on Requiem. They aren't facing anything they can't handle, but they are about to encounter the Prometheans, and that's where the third chapter (Forerunner) picks up.
As they're beginning to explore the planet, new technology is all around them. At this point it's not quite clear how this technology works, but it isn't anything they've seen before, and neither are the enemies. The Prometheans aren't your typical videogame enemies, either; they're not just cannon fodder for you to kill as you make your way through the game. Well, they might be if you're a very skilled player, but at least they're a bit more challenging to kill than the Covenant have become over the course of the Halo series.