As it happens, I was just caught up in reading some of the Halo lore on the wiki site devoted to it, which uses as sources the games, novels, graphic novels, and even the initial alternate-reality games like ILoveBees.
To many folks (my coworkers included), playing Halo for the story is a bit like reading Playboy for the articles - which is sad, because Bungie have a long, long history of making games with very intricate plots, usually with fan input and careful editing to make them relatively airtight compared to the settings of most games. Bungie’s fascination with numerology is also pretty notable.
The definition of ‘hero’ can be argued for centuries, but since the OP references ‘Master Chief from Halo’ and not just ‘from the Halo games,’ I think it’s fair to look at his entire story as it appears in all canon entries (warning spoilers whatever).
Honestly, it’s almost unrealistic how perfect they make the Master Chief out to be in the story - he’s served for decades, he’s earned nearly every medal possible, and he hates leaving anyone behind–even violating orders to protect his squadmates. Of course, he’s also been augmented with super strength and reflexes, and wields one of the most powerful suits of armor designed by the human military.
This, coupled with the fact that he never takes his helmet off, make him a pretty unique avatar among FPS games - sure, there’s never been a game where you’re actually supposed to be the scared grunt in a rank-and-file who always follows along and never actually leads a charge, but Halo is one of the only games to give a long character history (backed up by its own fictional science) as to why you, the player, are a near-invincible badass when you’re controlling Spartan 117.
So I’d say he’s definitely a hero, almost to a ridiculous extent - watch some of the Halo 3 commercials from a couple of years ago to see the lengths the canon around the Human-Covenant war was expounded upon for some examples. The marketing campaign’s theme was “Believe,” and the overall message boiled down to, ‘Believe that a lone super-soldier can turn the battle around, fend off the zealous Covenant and the infectious Flood, and prevent the destruction of all sentient life.’
Pretty over-the-top, but definitely well into the ‘hero’ category, when you count some of the tough decisions made in the later games and books.