MP2/6-31+G(d) calculations are used to compare the static electronic first hyperpolarizability (β) of planar and twisted sesquifulvalenes. The longitudinal component of β which is dominant in both structures is more than five times larger in the twisted form where it points in the opposite direction from the dipole moment. This larger β value can be related to the much larger second-order charge derivatives with respect to an electric field. Moreover, using the SOS scheme, the β of the twisted form is shown to originate from a single low-lying excited state characterized by the transfer of one electron from the five-membered to the seven-membered ring. The enhancement due to twisting supports the phenomenon of sudden polarization in polar hydrocarbons and leads to β values that are of the same order of magnitude as in push-pull conjugated polyenes of similar size. Our analysis suggests that substituting the inter-ring carbon atoms by heteroatoms will result in substantial changes in β.