Switching events in the current flowing through individual redox proteins, (azurin) spontaneously wired between two electrodes, are studied using an electrochemical scanning tunneling microscope (ECSTM). These switching events in the current-time trace are characterized using conductance histograms, and reflect the intrinsic redox thermodynamic dispersion in the azurin population. This conductance switching may pose limitations to miniaturizing redox protein-based devices.