The rotation of the plane of polarization of linearly polarized light by chiral molecules in solution is due to a forward scattering event. Ordinary optical rotation, a single-photon effect, is independent of intensity. As the light intensity is increased, other effects can appear, such as two-photon scattering or alignment of the molecule by one photon and scattering with a change of polarization by another. Both of these effects result in intensity-dependent (or nonlinear) optical rotation. A polarimeter was used to measure the nonlinear optical rotation of solutions in a heterodyne experiment. No nonlinear optical rotation was found in molecules lacking an absorption band near the laser frequency. In the three pyrimidine nucleosides studied, which do have such an absorption band, a nonlinear optical rotation was identified that was cumulative with each laser pulse. The effect persisted with a time constant that was on the order of seconds and characteristic of the molecule.