<p>I introduce a lattice gas model with excluded volume interactions and investigate its phase behavior on the square lattice. Monte Carlo simulations and finite-size scaling show a discontinuous sub-lattice ordering transition towards a high-density solidlike phase characterised by an anti-ferromagnetic dimerized ground state with eightfold degeneracy. Since thermodynamics is controlled by entropy alone this provides a simple athermal realization of a dimerization process. Interestingly, the model can be considered as a special case of a family of hard-core lattice gases with local geometric constraints on both particles and vacancies, which generalizes the one proposed by Biroli and Mézard in the context of glassy systems.</p>