  We have studied semileptonic $B$ meson decays with a P-wave charm meson in
the final state using 3.29 x 10^6 B\bar{B} events collected by the CLEO~II
detector at the Cornell Electron-positron Storage Ring. We find a value for the
exclusive semileptonic product branching fraction: Br(B^- -> D_1^0 l^-
\bar{\nu}) x Br(D_1^0 -> D^{*+}\pi^-) = (0.373 \pm 0.085 \pm 0.052 \pm 0.024)%
and an upper limit for Br(B^- -> D_2^{*0} l^- \bar{\nu}) x Br(D_2^{*0} ->
D^{*+}\pi^-) < 0.16%$ (90% C.L.). These results indicate that at least 20% of
the total B^- semileptonic rate is unaccounted for by the observed exclusive
decays, B^- -> D^0 l^- \bar{\nu}, B^- -> D^{*0} l^- \bar{\nu}, B^- -> D_1^0 l^-
\bar{\nu}, and B^- -> D_2^{*0} l^- \bar{\nu}.
