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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 $1.8 \times 10^{-6}$.
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