Measurement of the decays B--> phiK and B--> phiK*

We have observed the decays B--> phiK and phiK(*) in a sample of over 45 million B mesons collected with the BABAR detector at the PEP-II collider. The measured branching fractions are B(B+--> phiK+) = (7.7(+1.6)(-1.4)+/-0.8)x10(-6), B(B0--> phiK0) = (8.1(+3.1)(-2.5)+/-0.8)x10(-6), B(B+--> phiK(*+)) = (9.7(+4.2)(-3.4)+/-1.7)x10(-6), and B(B0--> phiK(*0)) = (8.7(+2.5)(-2.1)+/-1.1)x10(-6). We also report the upper limit B(B+--> phipi(+))<1.4x10(-6) ( 90% C.L.).