  We report the first observation of radiative decay B^0 -> \phi K^0 \gamma
using a data sample of 772x10^6 BBar pairs collected at the Y(4S) resonance
with the Belle detector at the KEKB asymmetric-energy e+e- collider. We observe
a signal of 35+/-8 events with a significance of 5.4 standard deviations
including systematic uncertainties. The measured branching fraction is ${\cal
B}(B^0 -> \phi K^0 \gamma) = (2.66\pm 0.60 \pm 0.32) \times 10^{-6}$. We also
precisely measure ${\cal B}(B^+ -> \phi K^+ \gamma) = (2.34\pm 0.29 \pm 0.23)
\times 10^{-6}$. The uncertainties are statistical and systematic,
respectively. The observed M_{\phi K} mass spectrum differs significantly from
that expected in a three-body phase-space decay.
