Nanocrystalline La0.7 Sr0.3 Mn O3 films with thickness t=10-60 nm were grown on LaAl O3 (100) substrates by radio-frequency magnetron sputtering. Their electrical resistivity and low-field magnetoresistance (MR) were measured. Metal-insulator transitions occur above 275 K for films with t=20-60 nm, but the electron localization prevails in the 10 nm thick film. Furthermore, only the 10 nm thick film has an MR that depends on the inverse of temperature, consistent with the model of spin-polarized tunneling. This relationship may reflect a critical aspect of the structure of graingrain-boundaries. Accordingly, the tunneling MR in this film is 27% at 75 K.