  I study a dimer model on the square lattice with nearest-neighbor exclusion
as the only interaction. Detailed simulations using tomographic entropic
sampling show that as the chemical potential is varied, there is a strongly
discontinuous phase transition, at which the particle density jumps by about
18% of its maximum value, 1/4. The transition is accompanied by the onset of
orientational order, to an arrangement corresponding to the {1/2,0,1/2}
structure identified by Phares et al. [Physica B {\bf 409}, 1096 (2011)] in a
dimer model with {\it finite} repulsion at {\it fixed} density. Using
finite-size scaling and Binder's cumulant, the expected scaling behavior at a
discontinuous transition is verified in detail. The discontinuous transition
can be understood qualitatively given that the model possesses eight equivalent
maximum-density configurations, so that its coarse-grained description
corresponds to that of the q=8 Potts model.
