We observe a narrow enhancement near 2m(p) in the invariant mass spectrum of pp pairs from radiative J/psi-->gammapp decays. No similar structure is seen in J/psi-->pi(0)pp decays. The results are based on an analysis of a 58 x 10(6) event sample of J/psi decays accumulated with the BESII detector at the Beijing electron-positron collider. The enhancement can be fit with either an S- or P-wave Breit-Wigner resonance function. In the case of the S-wave fit, the peak mass is below 2m(p) at M=1859(+3)(-10) (stat)+5-25(syst) MeV/c(2) and the total width is Gamma<30 MeV/c(2) at the 90% confidence level. These mass and width values are not consistent with the properties of any known particle.