It has been a great challenge to measure the spectrum of pure bound-electronic third-order nonlinear refraction (n(2)) of organic chromophores in solutions because of the spurious contribution from the solvent and cuvette walls. In order to circumvent this problem, we present here a new method to obtain a highly accurate absolute n(2) value of organic molecules in solutions with a self-referenced nonlinear ellipse rotation (NER) technique. As a proof of concept, we measured n(2) spectra of two well-known chromophores, rhodamines B and 6G dissolved in methanol, in the range from similar to 600 to 1200 nm. Our results pointed out that these two dyes present similar dispersion curves with strong negative nonlinearities near the one-photon absorption band and small positive values at long wavelengths. Furthermore, the negative signal of the dyes can be strong enough to cancel and even invert the positive nonlinear refraction of the solvent (methanol) as the solution's concentration increases. To understand the n(2) spectrum and its connection to molecular properties of organic chromophores, we employed the sum-over-states (SOS) approach within the few-energy-level model and observed an excellent agreement between the experimental and theoretical spectra. In this way, we believe that, employing our NER technique and the SOS model, it is possible to determine both experimentally and theoretically the absolute magnitude and spectra of pure electronic n(2) for a large variety of other organic molecules.