  We construct a quantum extension of the (classical) three-coloring model
introduced by Baxter [J.Math.Phys.11, 784 (1970)] for which the ground state
can be computed exactly along a continuous line of Rokhsar-Kivelson solvable
points. The quantum model, which admits a local spin representation, displays
at least three different phases; an antiferromagnetic (AF) phase, a line of
quantum critical points, and a ferromagnetic (F) phase. We argue that, in the
ferromagnetic phase, the system cannot reach dynamically the quantum ground
state when coupled to a bath through local interactions, and thus lingers in a
state of quantum glassiness.
