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We analyzed the glassy-state structural relaxation of polymers near surfaces and interfaces by monitoring fluorescence in multilayer films. Relative to that of bulk, the rate of structural relaxation of poly(methyl methacrylate) is reduced by a factor of 2 at a free surface and by a factor of 15 at a silica substrate interface; the latter exhibits a nearly complete arresting of relaxation. The distribution in relaxation rates extends more than 100 nanometers into the film interior, a distance greater than that over which surfaces and interfaces affect the glass transition temperature.