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We present results of molecular dynamics simulations for a supercooled polymer melt confined between two smooth and purely repulsive walls. The thickness D of the him is about 7 times the bulk radius of gyration. For all temperatures studied, a significant increase of the monomer and chain mobilities with respect to the bulk is observed. Preliminary results suggest that structural relaxation times exhibit a power-law behavior in the vicinity of a critical temperature T_c(D) approximate to 0.39 (in Lennard-Jones units). This estimate of T_c(D) is about 14% smaller than the corresponding bulk value. Despite this significant decrease the time dependence of various mean-square displacements seems to be unaffected by confinement if data for the same reduced temperatures T - T_c of the bulk and the film are compared.