  We report the first observation of the radiative decay B^0 -> \phi K^0 \gamma
using a data sample of 772 x 10^6 B B-bar pairs collected at the \Upsilon(4S)
resonance with the Belle detector at the KEKB asymmetric-energy e^+e^-
collider. We observe a signal of 37+/-8 events with a significance of 5.4
standard deviations including systematic uncertainties. The measured branching
fraction is ${\cal B}(B^0 -> \phi K^0 \gamma) = (2.74\pm 0.60 \pm 0.32) \times
10^{-6}$, where the uncertainties are statistical and systematic, respectively.
We also report the first measurements of time-dependent CP violation
parameters: ${\mathcal S}_{\phi K_S^0 \gamma} = +0.74^{+0.72}_{-1.05}
(stat)^{+0.10}_{-0.24} (syst)$ and ${\mathcal A}_{\phi K_S^0 \gamma} = +0.35
+/- 0.58 (stat)^{+0.23}_{-0.10} (syst)$. Furthermore, we measure ${\mathcal
B}(B^+ -> \phi K^+ \gamma) = (2.48 +/- 0.30 +/- 0.24) x 10^{-6}$, ${\mathcal
A}_{CP} = -0.03 +/- 0.11 +/- 0.08$ and find that the signal is concentrated in
the M_{\phi K} mass region near threshold.
