Neoclassical transport in the presence of large ion orbits is investigated. The study is motivated by the recent experimental results that ion thermal transport levels in enhanced confinement tokamak plasmas fall below the “irreducible minimum level” predicted by standard neoclassical theory. This apparent contradiction is resolved in the present analysis by relaxing the basic neoclassical assumption that the ions orbital excursions are much smaller than the local toroidal minor radius and the equilibrium scale lengths of the system. Analytical and simulation results are in agreement with trends from experiments. The development of a general formalism for neoclassical transport theory with finite orbit width is also discussed.