By the power of truth, I, while living, have conquered the universe.
Posted by: BungiePress
No, he's very much alive. His fate is revealed after two occurrences. Your beating of Legendary or watching Origins Part 1 and 2 of Halo: Legends (DVD).
When half of the ship made it through the slipspace rupture the other half was lost in the depths of space.
Chief is currently in the half that didn't make it through the teleportation. So he's in Cryo Sleep and being monitored by Cortana.
His last lines from the game, I'm pretty sure were: "Wake me when you need me" /paraphrase.
So if you want to see this first hand. Beat Legendary, otherwise...
http://www.youtube.com/watch?v=pQjefkVXfU0
Er... John and Cortana did make it through the Portal, she says:
"We made it through the portal just as it collapsed."
Mendicant Bias altered the course for John, the final Terminal reveals that he's sending him to the Forerunners to prove he has atoned.