Epitaxial Tl2Ca2Ba2Cu3O10 films on (100) LaAlO3 are prepared by post-annealing 2Tl:2Ca:2Ba:3Cu precursor films at 830–860 °C in 0.03–0.15 atm of O2. These films (0.2–1.1 µm thickness) are smooth and shiny to the eye, and have a sharp zero resistance and onset diamagnetic transition temperature of 117–121 K. Transport critical current densities of 1.6×106 A/cm2 at 77 K and 105 A/cm2 at 100 K are obtained for a 0.38-µm-thick film in magnetic fields up to 100 Oe. Strong flux pinning at low temperatures is inferred from the weak-field dependence of the critical current density calculated from magnetic hysteresis loops. At 5 K, the best film has a magnetic critical current density of 9×106 A/cm2 in zero field, decreasing gradually to 1.5×106 A/cm2 in a 5-T field. Applied Physics Letters is copyrighted by The American Institute of Physics.