The Collaborative International Dictionary of English v.0.48:

Uniat \U"ni*at\, Uniate \U"ni*ate\, n. (Eccl.)
   A member of the Greek Church, who nevertheless acknowledges
   the supremacy of the Pope of Rome; one of the United Greeks.
   Also used adjectively.
   [1913 Webster]

WordNet (r) 3.0 (2006):

Uniat
    n 1: a member of the Uniat Church [syn: Uniat, Uniate,
         Uniate Christian]