  We present evidence for the flavor-changing neutral current decay $B\to
K^*\ell^+\ell^-$ and a measurement of the branching fraction for the related
process $B\to K\ell^+\ell^-$, where $\ell^+\ell^-$ is either an $e^+e^-$ or
$\mu^+\mu^-$ pair. These decays are highly suppressed in the Standard Model,
and they are sensitive to contributions from new particles in the intermediate
state. The data sample comprises $123\times 10^6$ $\Upsilon(4S)\to B\bar{B}$
decays collected with the Babar detector at the PEP-II $e^+e^-$ storage ring.
Averaging over $K^{(*)}$ isospin and lepton flavor, we obtain the branching
fractions ${\mathcal B}(B\to K\ell^+\ell^-)=(0.65^{+0.14}_{-0.13}\pm
0.04)\times 10^{-6}$ and ${\mathcal B}(B\to
K^*\ell^+\ell^-)=(0.88^{+0.33}_{-0.29}\pm 0.10)\times 10^{-6}$, where the
uncertainties are statistical and systematic, respectively. The significance of
the $B\to K\ell^+\ell^-$ signal is over $8\sigma$, while for $B\to
K^*\ell^+\ell^-$ it is $3.3\sigma$.
