  The cross section for coherent $\omega$-meson photoproduction off the
deuteron has been measured for the first time as a function of the momentum
transfer $t = (P_{\gamma}-P_{\omega})^2$ and photon energy $E_{\gamma}$ using
the CLAS detector at the Thomas Jefferson National Accelerator Facility. The
cross sections are measured in the energy range $1.4 < E_{\gamma} < 3.4$ GeV. A
model based on $\omega-N$ rescattering is consistent with the data at low and
intermediate momentum transfer, $|t|$. For $2.8 < E_{\gamma} < 3.4$ GeV, the
total cross-section of $\omega-N$ scattering, based on fits within the
framework of the Vector Meson Dominance model, is in the range of 30-40 mb.
