We report on a measurement of phi-meson production in Au+Au collisions at a beam momentum of 11.7 A GeV/c by Experiment E917 at the AGS. The measurement covers the midrapidity region 1.2 < y < 1.6. Transverse-mass spectra and the rapidity distribution are presented as functions of centrality characterized by the number of participant projectile nucleons. The yield of phi's per participant projectile nucleon increases strongly in central collisions in a manner similar to that observed for kaons. Comment: 12 pages, 3 table, 14 eps figures which use \includegraphics, revtex 4, revised version submitted to Phys. Rev. C