Magnetic relaxation in a polycrystalline Hg0_8Tl0.2Ba2Ca2Cu30s+6 [(Hg,Tll-1223] superconductor was measured in the temperature range 1.85-20 K with different magnetic fields applied during the cooling process. The relaxation curves show a nearly perfect linear ln(t) behavior. The temperature dependence of the normalized relaxation rate, R = Id (M /M0)/dln(t)I, was studied for two applied magnetic fields. With the lower applied field (H.= 3 kOe), a temperature-independent R is found below 2.1 K and ex­plained in terms of quantum tunneling of vortices. As the applied field increases (H. = 10 kOe), the tran­sition from the thermal to the quantum regime is not found in the experimentally accessible temperature range above 1.85 K. The field dependence of R at 2.8 K is studied in order to analyze the dimensionality of the flux-line lattice.