We search for the rare flavor-changing neutral-current decay B(+)--> K(+)nunu in a data sample of 82 fb(-1) collected with the 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 B(B(+)-->K(+)nunu ) < 5.2 x 10(-5) at the 90% confidence level. In addition, by selecting for pions rather than kaons, we obtain a limit of B(B+-->pi(+)nunu) < 1.0 x 10(-4) using only the hadronic B reconstruction method.