Chief rarely talks at all, Caboose. And he does have friends. Cortana, Johnson, Blue Team, and yes, the Arbiter. He rarely responded verbally to any of them. But he showed genuine care for them.
At the start of Halo 3, it was an uneasy alliance. As it went on, they formed trust, which grew with time. By the time they got to Truth, Chief had the respect for him to allow him to be the one to kill Truth. Immediately afterward, they stood back to back like brothers. And after that, the Arbiter even went to High Charity after Chief, to help him!
Then the Arbiter alone stuck by Chief to see the mission to the end, even when given the option not to, and when the other Elites were already leaving. And he showed sympathy when Johnson died, despite rarely being fazed by death normally.
And of course, the line from the prologue. Which is canon no matter how you look at it. If the implications in Halo 3 were not enough, Halo 2 Anniversary confirms it. They do count each other friends.