We present a preliminary search for the flavor-changing neutral current decay B^+ -> K^+ nunubar using 56 million Y(4S) decays recorded with the BABAR detector at the SLAC B factory. Identification of the B^+ -> K^+ nunubar final state, with two neutrinos, requires the reconstruction of the companion B in the event. The companion B is reconstructed in the decay mode B^- -> D^0 l^- nubar X, which provides both high efficiency and good purity. The particles not used in the reconstruction of the companion B are compared with the signature expected for B^+ -> K^+ nunubar decays. Two candidates are found in the data with an expected background of 2.2 events. Under the assumption that all candidates are signal events, an upper limit on the branching fraction for B^+ -> K^+ nunubar of 9.4 x 10^-5 at 90% confidence level is determined.