We study the dynamics of a one-dimensional fluid of orientable hard rectangles with a non-coarse-grained microscopic mechanism of facilitation. The length occupied by a rectangle depends on its orientation, which is a discrete variable coupled to an external field. The equilibrium properties of our model are essentially those of the Tonks gas, but at high densities the orientational degrees of freedom become effectively frozen due to jamming. This is a simple analytically tractable model of the glassy phase. Under a cyclic variation of the pressure, hysteresis is observed. Following a pressure quench, the orientational persistence exhibits a two-stage decay characteristic of glassy systems.