Microscopic studies of the electrochemical deposition of Cu on 1T-TaS2 from CuSO4 solution are presented that reveal the formation of self-organized networks of nanotunnels on the substrate surface. Similar as for deposition under ultrahigh vacuum conditions, straight tunnels with a prismatic cross section along the crystallographic directions as well as more irregular buckles are formed. Tunnel formation commences only after deposition and emersion from the electrolyte on time scales between minutes and days, depending on the deposition conditions. It is strongly promoted by negative deposition potentials, suggesting an intercalaction-driven formation mechanism. (C) 2008 The Electrochemical Society.