Measurement of dijet photoproduction events with rapidity gaps with ZEUS at HERA Photoproduction dijet events with a large rapidity gap between the jets were studied with the ZEUS detector at HERA using an integrated luminosity of 39 pb-1. Rapidity gaps are defined in terms of the energy flow between the jets, the requirement being that the total sum of transverse energy in this region is less than E_T^{CUT}. The data show a clear excess over the predictions of standard photoproduction models. This is interpreted as evidence for the exchange of a strongly interacting color-singlet object. Monte Carlo models including such a color-singlet exchange are able to describe the data.