Here, we report on the assembly of thymine molecules into extended straight chains of single and multiple dimer rows on a Si(111)/Ag Ö3×Ö3\sqrt{3}\times \sqrt{3} R30° surface. Using variable temperature scanning tunneling microscopy, we follow the nucleation process and formation of self-assembled structures. Submonolayer coverages at 120 K are disordered and exhibit a high density of thymine dimers. Upon annealing the dimers assemble into extended dimer chains along three equivalent high-symmetry surface directions. At low coverages single dimer rows are favored. At increased coverage chains with multiple dimer rows are observed, with a preference to an even multiplicity. We show that a complex cross-talk between H-bond thymine–thymine interactions and commensurization of dimer chains to the Ag/Si surface leads to this specific layout.