Using a low-temperature scanning tunneling microscope (STM), we observe that Co adatoms are unusually strongly bound to a particular type of pinning centers on the Cu(111) surface. Using density-functional-theory calculations, the pinning centers are identified as Ag substitutional atoms embedded in the topmost atomic layer of the surface. These impurities are hardly detectable in the STM images as they have low topographic height and produce no standing-wave patterns. They do not affect the exchange coupling of the Co adsorbate with the substrate electrons; thus, the Kondo resonances measured on pinned and free Co adatoms show no detectable differences. Whereas free Co adatoms undergo significant surface diffusion already above 8 K, Ag-stabilized Co adatoms remain pinned up to 12.7 K.