An enhancement near the m(p)+M(Lambda) mass threshold is observed in the combined pLambda and pLambda invariant-mass spectrum from J/psi-->pK(-)Lambda;+c.c. decays. It can be fit with an S-wave Breit-Wigner resonance with a mass m=2075+/-12(stat)+/-5(syst) MeV and a width of Gamma=90+/-35(stat)+/-9(syst) MeV; it can also be fit with a P-wave Breit-Wigner resonance. Evidence for a similar enhancement is also observed in psi(')-->pK(-)Lambda;+c.c. decays. The analysis is based on samples of 5.8x10(7)J/psi and 1.4x10(7)psi(') decays accumulated in the BES II detector at the Beijing Electron-Positron Collider.