This is one of the more complicated and controversial questions in Halo's history. The short answer is that it is both.
Halo was originally announced as a third-person game. At the time, Bungie was also developing another third-person game, Oni.
The original rationale for third-person was that it allowed the player to see things happening to his character and around him. When you're in first person, you can't see things like your armor being charred by explosions, or your body reacting to impacts. Bungie claimed to have addressed the difficulties inherent in third person aiming with a better aiming system-- and part of that system appeared to be visible in some of the movies of Halo released last year.
However, by the time Bungie was purchased by Microsoft, the balance of play was switching towards a first-person perspective.
In its current form to be released on the Xbox in November of 2001, the third-person perspective is used only for piloting vehicles. It is apparently not user-selectable. It is not known whether this will change in the release for the Windows and Macintosh platforms.