  We have studied two-body charmless hadronic decays of $B$ mesons into the
final states phi K and phi K^*. Using 9.7 million $B\bar{B}$ pairs collected
with the CLEO II detector, we observe the decays B- -> phi K- and B0 -> phi K*0
with the following branching fractions: BR(B- -> phi K-)=(5.5 +2.1-1.8 +- 0.6)
x 10^{-6} and BR(B0 -> phi K*0)=(11.5 +4.5-3.7 +1.8-1.7) x 10^{-6}. We also see
evidence for the decays B0 -> phi K0 and B- -> phi K*-. However, since the
statistical significance is not overwhelming for these modes we determine upper
limits of <12.3 x 10^{-6} and <22.5 x 10^{-6} (90% C.L.) respectively.
