We present the first observation of the decay B --> J/psi phi K. Using 9.6
X 10(6) B (B) over bar meson pairs collected with the CLEO detector, we hav
e observed ten fully reconstructed B --> J/psi phi K candidates, whereas th
e estimated background is 0.5 +/- 0.2 event. We obtain a branching fraction
of B(B --> J/psi phi K) = (8.8(-3.0)(+3.5)[stat] +/- 1.3[syst]) X 10(-5).
This is the first observed B meson decay requiring the creation of an addit
ional s (s) over bar quark pair.