  The reaction gamma p -> J/Psi p has been studied in ep interactions using the
ZEUS detector at HERA. The cross section for elastic J/Psi photoproduction has
been measured as a function of the photon-proton centre of mass energy W in the
range 40 < W < 140 GeV at a median photon virtuality Q^2 of 5*10^{-5} GeV^2.
The photoproduction cross section, sigma_{gamma p -> J/Psi p}, is observed to
rise steeply with W. A fit to the data presented in this paper to determine the
parameter $\delta$ in the form sigma_{gamma p -> J/Psi p} \propto W^{\delta}
yields the value \delta = 0.92 \pm 0.14 \pm 0.10. The differential cross
section dsigma/d|t| is presented over the range |t| < 1.0 GeV^2 where t is the
square of the four-momentum exchanged at the proton vertex. d\sigma/d|t| falls
exponentially with a slope parameter of 4.6 \pm 0.4 (+0.4-0.6) GeV^{-2}. The
measured decay angular distributions are consistent with s-channel helicity
conservation.
