A study of the Okubo-Zweig-Iizuka (OZI) rule has been performed in a high-energy photon beam by comparing the production ratios of exclusive meson final states. Measurement of the ratio $\frac{\ensuremath{\sigma}(\ensuremath{\gamma}A\ensuremath{\rightarrow}\ensuremath{\varphi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}A)}{\ensuremath{\sigma}(\ensuremath{\gamma}A\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}A)}=0.10\ifmmode\pm\else\textpm\fi{}0.02$ is evidence that the OZI rule does not suppress this photoproduction reaction to the extent observed in $\ensuremath{\varphi}$ decays and in production by hadrons. The ratios of other exclusive photoproduction reactions are also presented.