We report the induction of homochirality in enantiomorphous layers of achiral succinic acid on a Cu(110) surface after doping with tartaric acid (TA) enantiomers. Succinic acid becomes chiral upon adsorption due to symmetry-breaking interactions with the Cu(110) surface. The doubly deprotonated bisuccinate forms mirror domains on the surface, which leads to a superposition of (11,-90) and (90,-11) patterns observed by low-energy electron diffraction (LEED). On average, however, the surface layer is racemic. An amount of 2 mol % of (R,R)- or (S,S)-tartaric acid in the monolayer, corresponding to an absolute coverage of 0.001 tartaric acid molecule per surface copper atom, is sufficient to make the LEED spots of one enantiomorphous lattice disappear. After thermally induced desorption of TA, the succinic acid lattice turns racemic again. In analogy to the "sergeants-and-soldiers" principle described for helical polymers, this effect is explained by a lateral cooperative interaction within the two-dimensional lattice.