Search for B+ --> K+l+l- and B⁰ --> K(*0)l+l-

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Using a sample of 3.7 x 10⁶ Y(4S) --> B-anti-B events collected with the BABAR detector at the PEP-II storage ring, we search for the electroweak penguin decays B+ --> K+e+e-, B+ --> K+mu+mu-, B⁰ --> K*0)e+e-, and B⁰ --> K*0)mu+mu-. We observe no significant signals for these modes and set preliminary 90% C.L. upper limits of B(B+ --> K+e+e-) < 12.5 x 10⁻⁶, B(B+ --> K+mu+mu-) < 8.3 x 10⁻⁶, B(B⁰ --> K*0)e+e-) < 24.1 x 10⁻⁶, B(B⁰ --> K*0)mu+mu-) < 24.5 x 10⁻⁶.