  We present a search for the decay $B^+ \rightarrow a_1^+(1260) K^{*0}(892)$.
The data, collected with the \mbox{\slshape B\kern-0.1em{\smaller A}\kern-0.1em
B\kern-0.1em{\smaller A\kern-0.2em R}} detector at the SLAC National
Accelerator Laboratory, represent 465 million $B\overline{B}$ pairs produced in
$e^+e^-$ annihilation at the energy of the $\Upsilon(4s)$. We find no
significant signal and set an upper limit at 90\%\ confidence level on the
product of branching fractions {\cal B}(B^+ \rightarrow a_1^+(1260)
K^{*0}(892)) \times {\cal B}(a_1^+(1260) \rightarrow \pi^+ \pi^- \pi^+) of $1.8
\times 10^{-6}$.
