  We search for the rare flavor-changing neutral-current decay $B^+ \to K^+ \nu
\bar{\nu}$ in a data sample of 82 fb$^{-1}$ collected with the {\sl BABAR}
detector at the PEP-II B-factory. Signal events are selected by examining the
properties of the system recoiling against either a reconstructed hadronic or
semileptonic charged-B decay. Using these two independent samples we obtain a
combined limit of ${\mathcal B}(B^+ \to K^+ \nu \bar{\nu})<5.2 \times 10^{-5}$
at the 90% confidence level. In addition, by selecting for pions rather than
kaons, we obtain a limit of ${\mathcal B}(B^+ \to \pi^+ \nu \bar{\nu})<1.0
\times 10^{-4}$ using only the hadronic B reconstruction method.
