Hyper-Rayleigh light scattering measurements at incident wavelengths of 1064 and 1319 nm are reported for several organic nonlinear optical chromophores in solution with approximately 5%-10% uncertainty in the relative first hyperpolarizabilities. The measured chromophores include representatives from C-1, C-s, C-2V, and D-3 molecular point groups and include both neutral and ionic compounds. The measurements were made with 2-5 cm(-1) spectral resolution and include polarization analysis of the incident and scattered light. Polarization ratios were measured with 2%-3% uncertainty for each molecule, and relative magnitudes of the hyperpolarizability components were deduced. Two-photon induced fluorescence from several chromophores was observed to overlap with the scattered second harmonic light spectrum. The use of a scanning monochromator, however, generally allows the separation of these two sources of photons. The measured first hyperpolarizabilities are consistent with previous electric field induced second harmonic generation measurements of the same compounds, provided that the standard reference value for the nonlinear susceptibility of quartz is tab-Pn to be d(11)=0.30+/-0.02 pm/V at 1064 nm.