Time-logarithmic magnetic-relaxation measurements have been obtained in an epitaxial Tl 2 Ba 2 Ca 2 Cu 3 O x thin film for the zero-field cooled and remanent magnetization, with low and moderate applied magnetic fields. With low fields ( H a =50 Oe), the normalized magnetic relaxation rates, S≡‖d(M/ M i )/d lnt‖, are temperature independent below T≃3.4 K, and the transition from the thermal to the quantum regime appears to be quite sharp. With moderate fields ( H a =500 Oe), the transition becomes smooth and takes place at temperatures higher than with low fields, T≃7 K. This seems to indicate that the mechanism responsible for low-temperature relaxation would be nondissipative Hall tunneling of two-dimensional vortices, rather than dissipative vortex motion.