The surface structure and corrosion of alkanethiol-covered Cu(100) surfaces in 1 mM HCl was studied by in-situ scanning tunneling microscopy (STM) and complementary electrochemical measurements. The octanethiol (OT) and hexadecanethiol (HDT) monolayers were prepared by spontaneous adsorption from ethanolic solution onto an electropolished single crystal substrate and then immersed into 1 mM HCl solution at potentials between -0.16 and -0.26 V vs Ag/AgCl (KCl sat.). Samples prepared in this way exhibit a well-defined surface morphology, where atomically smooth Cu terraces, which are found also on thiol-free Cu(100), are covered by monoatomically high Cu islands and by pits. Keeping the potential in this regime causes slow Cu roughening via the formation of additional Cu monolayer islands and pits. This surface restructuring is probably caused by exchange of Cu or Cu-thiolates with the electrolyte. The onset of Cu corrosion is shifted anodically to potentials in the range -0.12 to -0.10 V, reflecting the inhibition by the thiol layer. Copper corrosion proceeds via the formation of many small etch pits and pronounced surface roughening. At higher potentials and/or after prolonged etch times only few larger pits are observed. Local Cu corrosion within these pits proceeds via a similar mechanism as on bare Cu(100), suggesting that the inhibiting thiol layer is completely removed at these places.