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We have studied two-body charmless hadronic decays of B mesons into the final states straight phiK and phiK(*). Using 9.7 million B&Bmacr; pairs collected with the CLEO II detector, we observe the decays B- --> phiK- and B0--> phiK(*0) with the following branching fractions: B(B--->phiK-) = (5.5(+2.1)(-1.8)+/-0.6)x10(-6) and B(B0--> phiK(*0)) …