We observed, for the first time, solar neutrinos in the 1.0-1.5 MeV energy range. We determined the rate of pep solar neutrino interactions in Borexino to be 3.1+ or -0.6 sub(stat)+ or -0.3 sub(syst) counts/(day times 100 ton). Assuming the pep neutrino flux predicted by the Standard Solar Model, we obtained a constraint on the CNO solar neutrino interaction rate of <7.9 counts/(day times 100 ton) (95% C.L.). The absence of the solar neutrino signal is disfavored at 99.97% C.L., while the absence of the pep signal is disfavored at 98% C.L. The necessary sensitivity was achieved by adopting data analysis techniques for the rejection of cosmogenic super(11)C, the dominant background in the 1-2 MeV region. Assuming the MSW-LMA solution to solar neutrino oscillations, these values correspond to solar neutrino fluxes of (1.6+ or -0.3)x10 super(8) cm super(-2)s super(-1) and <7.7x10 super(8) cm super(-2)s super(-1) (95% C.L.), respectively, in agreement with both the High and Low Metallicity Standard Solar Models. These results represent the first direct evidence of the pep neutrino signal and the strongest constraint of the CNO solar neutrino flux to date.