In-situ scanning tunneling microscopy (STM) observations of structural changes on Cu(100) electrode surfaces in 1 mM HCl solution at potentials far below Cu bulk dissolution are presented. Upon increasing the potential above -0.4 V (versus Ag/AgCl) a transition from a (1 x 1) to a c(2 x 2) structure is observed, which is accompanied by a rearrangement of the substrate surface via a step faceting/defaceting mechanism. During the transition the steps change reversibly from a random orientation and frizzy appearance in the (1 x 1)regime to predominantly [010]- and [001]-oriented steps with strongly reduced mobility of Cu step atoms in the presence of the c(2 x 2) structure. Our observations show that the preferred step orientation in the c(2 x 2) regime corresponds to an adsorbate-induced equilibrium structure, and does not result from the kinetics of Cu dissolution as previously suggested. According to electrochemical measurements, the changes in Cl coverage accompanying the transition are negligible, indicating that the vastly different step structure and dynamics are caused solely by the potential-induced onset of order within the adlayer.