The formation of extended electron states in one-dimensional nanostructures is of key importance for the function of molecular electronic devices. Here, we study the effects of strong electron-phonon interaction on the formation of extended electronic states in intentionally created Cl vacancy pairs and chains in a NaCl bilayer on Cu(111). The interaction between the vacancies was tailored by fabricating vacancy pairs and chains of different orientation and separation with atomic precision using vertical manipulation. Small vacancy separations led to the formation of quantum-well-like vacancy states and localized interface states. By using scanning tunneling spectroscopy, we measured their energy splitting and broadening as a function of the intervacancy separation. Remarkably, the energy splitting between the vacancy states is enlarged by level repulsion resulting from the phonon dressing of the electronic states, as evidenced by theory.