At the beginning of the TV series House, doctors Cameron, Chase and Foreman were already working for House. From what I remember there were a couple moments in the series where it's hinted that maybe Dr. Chase had been there the longest (for example, S02E17 when Dr. Chase was describing to Foreman what House was like several years ago when talking about House's obsession with a previous patient, Esther), but I don't recall it actually being mentioned who had been there for what amount of time (or, at the very least who had been there the longest/shortest).
According to these Wikia pages:
Robert Chase: "Chase was the longest serving fellow at the start of the series, having been on the team since 2002."
Allison Cameron: "Cameron was hired about six months before the start of the series" (as stated in the "Before the series" tab)
Eric Foreman: "Eric is the new hire, joining veterans Robert Chase and Allison Cameron."
See also this page:
Chase has been there the longest (this is stated in a piece cut out of the pilot but referred to as well in the episode "All In" when he talks of cases he was involved in early on and what he heard from a previous person on a Fellowship).