The radiative decay B-->phi K gamma is observed for the first time. The branching fraction for the charged B--->phi K- gamma decay mode is measured to be B(B--->phi K- gamma)=(3.4+/-0.9+/-0.4)x10(-6). The photon energy distribution for the B--->phi K- gamma decay is presented. The signal for the neutral B(0)-->phi K(0)gamma decay mode is not statistically significant and an upper limit, B(B(0)-->phi K(0)gamma)<8.3x10(-6) at 90% C.L., is set. The analysis is based on a data set of 90 fb(-1) collected by the Belle experiment at the e(+)e(-) asymmetric collider KEKB.
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