We present the first measurement of the reaction $\ensuremath{\gamma}p\ensuremath{\rightarrow}{a}_{2}{(1320)}^{0}\phantom{\rule{0.16em}{0ex}}p$ in the photon energy range 3.5--$5.5\phantom{\rule{0.16em}{0ex}}\mathrm{Ge}\mathrm{V}$ and four-momentum transfer squared $0.2<\ensuremath{-}t<2.0{\phantom{\rule{0.16em}{0ex}}\mathrm{Ge}\mathrm{V}}^{2}$. Data were collected with the CEBAF Large Acceptance Spectrometer detector at the Thomas Jefferson National Accelerator Facility. The ${a}_{2}$ resonance was detected by measuring the reaction $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\eta}p$ and reconstructing the ${\ensuremath{\pi}}^{0}\ensuremath{\eta}$ invariant mass. The most prominent feature of the differential cross section is a dip at $\ensuremath{-}t\ensuremath{\approx}0.55{\phantom{\rule{0.16em}{0ex}}\mathrm{Ge}\mathrm{V}}^{2}$. This can be described in the framework of Regge phenomenology, where the exchange degeneracy hypothesis predicts a zero in the reaction amplitude for this value of the four-momentum transfer.