  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
$\gamma p$ 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, $x_\gamma$, shows a strong peak near unity, consistent with LO QCD
Monte Carlo predictions. In the transverse energy and pseudorapidity range
$5\le \eTg < 10$ GeV, $-0.7 \le \eta^\gamma < 0.8$, $\eTj\ge 5$ GeV, and
$-1.5\le \eta^{jet}\le 1.8$, with $\xgO > 0.8,$ the measured cross section is
$15.3 \pm 3.8 \pm 1.8 pb$, in good agreement with a recent NLO calculation.
