A popular urban legend concerns the apparent flow of stained glass windows in medieval cathedrals, where the glass windows are commonly observed to be thicker at the bottom than they are at the top. Advances in glass transition theory and experimental characterization techniques now allow for us to address this urban legend directly. In this work, we investigate the dynamics of a typical medieval glass composition used in Westminster Abbey. Depending on the thermal history of the glass, the room temperature viscosity is on the order of 10(24) to 10(25) Pa.s, about 16 orders of magnitude lower than found in a previous study of soda lime silicate glass. This measurement is in quantitative agreement with a newly derived model for the composition dependence of the nonequilibrium viscosity of glass. Despite this significantly lower value of the room temperature viscosity, the viscosity of the glass is much too high to observe measurable viscous flow on a human time scale. Using analytical expressions to describe the glass flow over a wall, we calculate a maximum flow of similar to 1 nm over a billion years.