We search for the decays {ital B}{sup {minus}}{r_arrow}l{sup {minus}}{bar {nu}}{sub l} in a sample of 2.2{times}10{sup 6} charged {ital B} decays using the CLEO detector. We see no evidence for a signal in any channel and set upper limits on the branching fractions of {ital B}({ital B}{sup {minus}}{r_arrow}{tau}{sup {minus}}{bar {nu}}{sub {tau}}){lt}2.2{times}10{sup {minus}3}, {ital B}({ital B}{sup {minus}}{r_arrow}{mu}{sup {minus}}{nu}2;m{sub {mu}}){lt}2.1{times}10{sup {minus}5}, and {ital B}({ital B}{sup {minus}}{r_arrow}{ital e}{sup {minus}}{bar {nu}}{sub {ital e}}){lt}1.5{times}10{sup {minus}5} at the 90% confidence level.