Maxwell Montes, standing up to 7 km above the adjacent highland plateaus, constitute the highest mountain belt on Venus. Because the thickness of the crust is likely to be limited by the gabbro--garnet granulite--eclogite phase transitions, this relief is difficult to reconcile with the assumption of thermodynamic equilibrium and a standard Airy isostatic model. We explore the hypothesis that the crust-mantle boundary is not in phase equilibrium, but rather is rate limited by the temperature-dependent volume diffusion of the slowest ionic species. Under the simplifying assumption that the mountains formed by uniform horizontal shortening of the crust and lithospheric mantle at a constant rate, we solve the one-dimensional thermal evolution problem. The time-dependent density structure and surface elevation are calculated by assuming a temperature-dependent reaction rate and local Airy isostatic compensation. For a rate of horizontal strain of 10-15 s-1 or greater, the rise in temperature at the base of the crust during mountain formation is modest to negligible, the deepening lower crust is metastable, and surface elevation increases as the crust is thickened. For strain rates less than 10-16 s-1, in contrast, crustal temperature increases with time because of internal heat production, and the lower crust is more readily transformed to the dense eclogite assemblage. For such models a maximum elevation is reached during crustal shortening. While this maximum relief is 7 km or more for some models, a smaller density contrast between crust and mantle than assumed here (500 kg m-3) and incorporation of horizontal heat transport would lessen this value. We therefore favor formation of the mountain belt at a strain rate at least of order 10-15 s-1. By this reasoning, Maxwell Montes must be comparatively young, of order 50 Ma. ¿ American Geophysical Union 1993