We have searched a sample of 9.6×106 B¯B events for the flavor-changing neutral current decays B→Kℓ+ℓ- and B→K*(892)ℓ+ℓ-. We subject the latter decay to the requirement that the dilepton mass mℓℓ exceed 0.5 GeV. There is no indication of a signal. We obtain the 90% confidence level upper limits B(B→Kℓ+ℓ-) < 1.7×10-6 and B(B→K*(892)ℓ+ℓ-)mℓℓ>0.5Gev< 3.3×10-6. We also obtain an upper limit on the weighted average 0.65B B(B→Kℓ+ℓ-)+0.35B(B→K*(892)ℓ+ℓ-)mℓℓ>0.5Gev < 1.5×10-6. The weighted-average limit is only 50% above the standard model prediction.