We report a transport study of ultrathin BiSe topological insulators with thickness from one quintuple layer to six quintuple layers grown on sapphire by molecular beam epitaxy. At low temperatures, the film resistance increases logarithmically with decreasing temperature, revealing an insulating ground state. The insulating behavior becomes more pronounced in thinner films. The sharp increase of resistance with magnetic field, however, indicates the existence of weak antilocalization originated from the topological protection. We show that this unusual insulating ground state in the two-dimensional limit of topological insulators is induced by the combined effect of strong electron interaction and topological delocalization.