The Collaborative International Dictionary of English v.0.48:

Primacy \Pri"ma*cy\, n. [LL. primatia, fr. L. primas, -atis, one
   of the first or principal, chief, fr. primus first: cf. F.
   primatie. See Prime, a.]
   1. The state or condition of being prime or first, as in
      time, place, rank, etc., hence, excellency; supremacy.
      [R.] --De Quincey.
      [1913 Webster]

   2. The office, rank, or character of a primate; the chief
      ecclesiastical station or dignity in a national church;
      the office or dignity of an archbishop; as, the primacy of
      England.
      [1913 Webster]

WordNet (r) 3.0 (2006):

primacy
    n 1: the state of being first in importance