Transient birefringence can be induced in a gas of anisotropic molecules by an intense polarized laser pulse. We propose to use this birefringence to phase match nonlinear optical frequency-conversion processes. The conditions for anisotropic phase matching are derived, and experimental conditions required for phase-matched third-harmonic generation in a gas-filled hollow-core fiber are presented. We show that these conditions are experimentally feasible over a significant parameter range, making possible a new type of nonlinear optics.