Molecular chromophores with twisted pi-electron systems have been shown to possess unprecedented values of the quadratic hyperpolarizability, beta, with very large real parts and much smaller imaginary parts. We report here an experimental and theoretical study which shows that these twisted chromophores also possess very large values of the real part of the cubic hyperpolarizability, gamma, which is responsible for nonlinear refraction. Thus, for the two-ring twisted chromophore TMC-2 at 775 nm, relatively close to one-photon resonance, n(2) extrapolated to neat substance is large and positive (1.87 x 10(-13) cm(2)/W), leading to self-focusing. Furthermore, the third-order response includes a remarkably low two-photon absorption coefficient, which means minimal nonlinear optical losses: the T factor, alpha(2)lambda/n(2), is 0.308. These characteristics are attributed to closely spaced singlet biradical and zwitterionic states and offer promise for applications in all-optical switching.