Events containing an isolated prompt photon with high transverse energy, together with a balancing jet, have been observed for the first time in photoproduction at HERA. The data were taken with the ZEUS detector, in a γp centre of mass energy range 120-250 GeV. The fraction of the incoming photon energy participating in the production of the prompt photon and the jet, xγ, shows a strong peak near unity, consistent with LO QCD Monte Carlo predictions. In the transverse energy and pseudorapidity range 5 ≤ EγT < 10 GeV, -0.7 ≤ ηγ < 0.8, EjetT ≥ 5 GeV, and -1.5 ≤ ηjet ≤ 1.8, with xOBSγ > 0.8, the measured cross section is 15.3 ± 3.8 ± 1.8 pb, in good agreement with a recent NLO calculation. © 1997 Elsevier Science B.V.