We have performed a search for the decays B+-->J/psip(-)Lambda; and search for B0-->J/psip(-)p. in a data set of (88.9+/-1.0) x 10(6) Upsilon(4S) decays collected by the BABAR experiment at the PEP-II e(+)e(-) storage ring at the Stanford Linear Accelerator Center. Four charged B candidates have been observed with an expected background of 0.21+/-0.14 events. The corresponding branching fraction is (12(+9)(-6)) x 10(-6), where statistical and systematic uncertainties have been combined. The result can be interpreted as a 90% confidence level (C.L.) upper limit of 26 x 10(-6). We also find one B0 candidate, with an expected background of 0.64+/-0.17 events, implying a 90% C.L. upper limit of 1.9 x 10(-6).