The rare decay B → ?ll- is the simplest manifestation of a b → dl+l- flavor-changing neutral current (FCNC) process. This type of process only proceeds through penguin loop or box diagrams and is sensitive to physics at the electroweak scale. It can be used to constrain parameters of the Standard Model and its extensions. B → ?l+l- events have not yet been observed; the branching fraction is expected to be an order of magnitude smaller than the measured branching fraction for the similar B → Kl+l- decay. Using 230 million B$ar{B}$ meson pairs collected with the BABAR detector, we have done a search for the rare decay B →?l+l- . The data was produced in e+e- collision at the Y(4S) resonance in the PEP-II collider between 1999 and 2004. Four exclusive B-meson decay modes have been reconstructed: B+ → ?+l+l- and B0 → ?0l+l- , where l+ l- is either an electron pair (e+e-) or a muon pair (?+?-). We find no evidence for a signal, and we obtain upper limits on the branching fractions ?. Assuming the isospin relation ?(B+ → ?+l+l- ) 2 x ?B+/?B0 ?(B0 → ?0l+l-), we obtain an upper limit at 90% confidence level on the lepton-flavor-averaged branching fraction of B → ?l+l- to be ?(B → ?e?) 9.2 x 10sup-8 /supat 90% C.L. We have also reconstructed two control modes Bsup+/sup→ ?sup+/supesup±/sup?sup±/sup and Bsup0/sup → ?sup0/supesup±/sup?sup±/sup and we also obtain an upper limit at 90% confidence level on the lepton-flavor-violating decay B → ?e? of ?(B → ?e?) 9.2 x 10