Scanning tunneling microscopy measurements across isolated straight step edges on a Cu(111) surface were carried out for biases between 100 mV and 5 V. In addition to the well known surface state oscillations, and at lower sample bias than the onset of the two-dimensional surface image state, a sharply defined linear protrusion, was observed at the top of the step faces. This linear feature is interpreted as a one-dimensional image state at the step, with its energy modified by a dipolar potential whose appearance is attributed to Smoluchowski smoothing of the electron density at the step edge.