  We report a search for the rare decays $B^+ \to D^+ K^0$ and $B^+ \to D^+
K^{*0}$ in an event sample of approximately 465 million $B\bar B$ pairs
collected with the BaBar detector at the PEP-II asymmetric-energy $e^+e^-$
collider at SLAC. We find no significant evidence for either mode and we set
90\% probability upper limits on the branching fractions of $B(B^+ \to D^+ K^0)
< 2.9\times 10^{-6}$ and $B(B^+ \to D^+ K^{*0}) < 3.0\times 10^{-6}$.
