I doubt he's with them *all* the time, my suspicion is he comes and goes like their spouses/partners, but I believe the guy you are thinking of is a Church of Ireland (Anglican) priest named Jack Heaslip. He's been with the band for years, they met at Mount Temple where he taught before he went into the ministry and he did Bono and Ali's wedding. There's an MP3 out there on the net of him doing an opening blessing over the Elevation Tour at the last rehearsal in Miami.
@u2 also has an interview with Eugene Peterson, the guy who translated that Bible version Bono likes, _The Message_, and in it he refers to "their chaplain/pastor who was traveling with them" trying to set up a meeting between him and Bono last year. (Peterson says he was too busy <!!!> but he and Heaslip had a nice conversation.)