  J/Psi production in p+p collisions at sqrt(s) = 200 GeV has been Measured in
the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) over a
rapidity range of -2.2 < y < 2.2 and a transverse momentum range of 0 < pT < 9
GeV/c. The statistics available allow a detailed measurement of both the pT and
rapidity distributions and are sufficient to constrain production models. The
total cross section times branching ratio determined for J/Psi production is
B_{ll} sigma_pp^J/psi = 178 +/- 3(stat) +/- 53(syst) +/- 18(norm) nb.
