  We present the 1667 MHz OH megamaser luminosity function derived from a
single flux-limited survey. The Arecibo Observatory OH megamaser (OHM) survey
has doubled the number of known OH megamasers, and we list the complete catalog
of OHMs detected by the survey here, including three redetections of known
OHMs. OHMs are produced in major galaxy mergers which are (ultra)luminous in
the far-infrared. The OH luminosity function follows a power law in integrated
line luminosity, $\Phi \propto L_{OH}^{-0.64}$ per Mpc^3 per dex, and is
well-sampled for 10^{2.2} L(sun) < L_{OH} < 10^{3.8} L(sun). The OH luminosity
function is incorporated into predictions of the detectability and areal
density of OHMs in high redshift OH surveys for a variety of current and
planned telescopes and merging evolution scenarios parameterized by (1+z)^m in
the merger rate ranging from m=0 (no evolution) to m=8 (extreme evolution). Up
to dozens of OHMs may be detected per square degree per 50 MHz by a survey
reaching an rms noise of 100 microJy per 0.1 MHz channel. An adequately
sensitive ``OH Deep Field'' would significantly constrain the evolution
exponent m even if no detections are made. In addition to serving as luminous
tracers of massive mergers, OHMs may also trace highly obscured nuclear
starburst activity and the formation of binary supermassive black holes.
