The first measurement of the p n -> d omega total cross section has been achieved at mean excess energies of Q = 28 and 57 MeV by using a deuterium cluster-jet target. The momentum of the fast deuteron was measured in the ANKE spectrometer at COSY-Juelich and that of the slow spectator proton p(sp) from the p d -> p(sp) d omega reaction in a silicon telescope placed close to the target. The cross sections lie above those measured for p p -> p p omega but seem to be below theoretical predictions.