We present the first direct evidence for a supersonically moving steep ionization front in a solid density hot plasma. The plasma was produced by irradiating a transparent solid target with 100 fsec laser pulses at a peak intensity of 5 x 10(14) W/cm2. Time-resolved measurements of reflectivity, transmissivity, and frequency shift of a probe light, incident on the rear of the plasma, showed rapid formation of an over-dense plasma layer with a steep gradient that penetrates supersonically into the bulk target. Calculations using a simple nonlinear heat wave model, driven by electron thermal transport, show good agreement with the experimental results.