  The radiative decay $B \to \phi K \gamma$ is observed for the first time. The
branching fraction for the charged $B^- \to \phi K^- \gamma$ decay mode is
measured to be ${\cal B}(B^- \to \phi K^- \gamma) = (3.4 \pm 0.9 \pm 0.4)
\times 10^{-6}$. The photon energy distribution for the $B^- \to \phi K^-
\gamma$ decay is presented. The signal for the neutral $\bar{B}^0 \to \phi
\bar{K}^0 \gamma$ decay mode is not statistically significant and an upper
limit, ${\cal B}(\bar{B}^0 \to \phi \bar{K}^0 \gamma) < 8.3 \times 10^{-6}$ at
$90% {\rm CL}$, is set. The analysis is based on a dataset of 90 fb$^{-1}$
collected by the Belle experiment at the $e^+ e^-$ asymmetric collider KEKB.
