The impact of 3,3′ ′-thiobis(1-propanesulfonic acid, sodium salt) (TBPS) on Cu/Au(111) electrodeposition has been investigated by electrochemical methods and scanning tunneling microscopy (STM). Cyclic voltammetry and galvanostatic experiments indicate that Cu growth on Au(111) - which is known to be strongly kinetically hindered in additive-free, aqueous perchloric acid solutions - proceeds significantly faster in the presence of TBPS. The TBPS molecules either float on top of the growing film or become incorporated into the deposit. Complementary in situ STM studies show that Cu underpotential deposition (UPD) proceeds via two distinct mechanisms. One-dimensional growth of Cu stripes was observed between 0.05 and 0.35 V RHE for TBPS-modified Au(111) electrodes. Each stripe is composed of two or three parallel rows of Cu atoms oriented along the main crystallographic directions of the Au(111) substrate. An increase of the TBPS concentration near the solid/liquid interface restricts the Cu stripe growth to a narrow potential regime between 0.3 and 0.35 V RHE and two-dimensional Cu island growth becomes the favored growth mechanism. The latter fully dominates in TBPS-containing electrolyte. Cu growth in the overpotential deposition (OPD) regime results in a smooth Cu film with low surface roughness, in contrast to defect-mediated 3D island growth in additive-free electrolytes.