We study a phase transition in a 3D lattice gauge theory, a "coarse-grained" version of a classical dimer model. Duality arguments indicate that the dimer lattice theory should be dual to a XY model coupled to a gauge field with geometric frustration. The transition between a Coulomb phase with dipolar correlations and a long range ordered columnar phase is understood in terms of a Higgs mechanism. Monte Carlo simulations of the dual model indicate a continuous transition with exponents close but apparently different from those of the 3D XY model. The continuous nature of the transition is confirmed by a flowgram analysis.