The Collaborative International Dictionary of English v.0.48:

haj \haj\, hajj \hajj\n.
   A pilgrimage to Mecca; every Muslim must make this journey at
   least once. [Also spelled hadj.]

   Syn: hadj, haj.
        [WordNet 1.5] haji

The Collaborative International Dictionary of English v.0.48:

Hadj \Hadj\ (h[a^]j), n. [Ar. hajj, fr. hajja to set out, walk,
   go on a pilgrimage.]
   The pilgrimage to Mecca, performed by Mohammedans. It is the
   duty of Moslems to make a journey to Mecca at least once ina
   lifetime, or if that is not possible, three journeys to one
   of the alternate sacred sites. [Also spelled haj and
   hajj.]
   [1913 Webster +PJC]

WordNet (r) 3.0 (2006):

haj
    n 1: the fifth pillar of Islam is a pilgrimage to Mecca during
         the month of Dhu al-Hijja; at least once in a lifetime a
         Muslim is expected to make a religious journey to Mecca and
         the Kaaba; "for a Muslim the hajj is the ultimate act of
         worship" [syn: hajj, haj, hadj]