We report on a measurement of the branching ratio of the rare decay ω→ηγ relative to the well known decay ω→π0γ. The ω’s are produced in pp¯→ηω and pp¯→π0ω. Eigenstate mixing and interference effects of the ω and ρ0 are taken into account, as well as coherent interference with the background. We find evidence for the non-resonant annihilation channel B(pp¯→ηηγ)=(3.5±1.3)×10−5 and limit the value of B(ω→ηγ) to the range of (0.7to5.5)×10−4 depending on the degree of coherence with the background.Received 4 June 1999DOI:https://doi.org/10.1103/PhysRevD.61.032002©2000 American Physical Society