The interaction of a 3x10;{19} W/cm;{2} laser pulse with a metallic wire has been investigated using proton radiography. The pulse is observed to drive the propagation of a highly transient field along the wire at the speed of light. Within a temporal window of 20 ps, the current driven by this field rises to its peak magnitude approximately 10;{4} A before decaying to below measurable levels. Supported by particle-in-cell simulation results and simple theoretical reasoning, the transient field measured is interpreted as a charge-neutralizing disturbance propagated away from the interaction region as a result of the permanent loss of a small fraction of the laser-accelerated hot electron population to vacuum.