Through the use of an ultrashort (2 ps) optical probe, we have time resolved the propagation of an ionization wave into solid fused silica. This ionization wave results when a plasma is created by the intense irradiation of a solid target with a 2 ps laser pulse. We find that the velocity of the ionization wave is consistent with radiation driven thermal transport, exceeding the velocity expected from simple electron thermal conduction by nearly an order of magnitude.