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, x γ , shows a strong peak near unity, consistent with LO QCD Monte Carlo predictions. In the transverse energy and pseudorapidity range 5 ≤ E γ T < 10 GeV, −0.7 ≤ η γ < 0.8, E jet T ≥ 5 GeV, and −1.5 ≤ η jet ≤ 1.8, with x OBS γ > 0.8, the measured cross section is 15.3±3.8±1.8 pb, in good agreement with a recent NLO calculation.