Magnetization and high-resolution x-ray diffraction measurements of the Kitaev-Heisenberg material α-RuCl3 reveal a pressure-induced crystallographic and magnetic phase transition at a hydrostatic pressure of p∼0.2 GPa. This structural transition into a triclinic phase is characterized by a very strong dimerization of the Ru-Ru bonds, accompanied by a collapse of the magnetic susceptibility. Ab initio quantum-chemistry calculations disclose a pressure-induced enhancement of the direct 4d-4d bonding on particular Ru-Ru links, causing a sharp increase of the antiferromagnetic exchange interactions. These combined experimental and computational data show that the Kitaev spin-liquid phase in α-RuCl3 strongly competes with the crystallization of spin singlets into a valence bond solid.