We used neutron reflectivity to measure the interfacial width in the immiscible system polystyrene/poly(n-butyl methacrylate) (PS/PnBMA). Measurements were made on the same samples at temperatures ranging from below the glass-transition temperature (T-g) of PS to slightly above. We observed significant broadening of the interface at temperatures below the T-g of PS, indicating chain mobility below the bulk T-g value. The interfacial width exhibited a plateau at a value of 20 Angstrom in the temperature range of 365 K < T < 377 K. A control experiment involving hydrogenated and deuterated PS films (hPS/dPS) showed no such broadening over the same temperature region. The results are consistent with a reduction of the T-g of PS in the interfacial region of similar to 20 K.