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We show numerically that including soft-sphere type collisions in the celebrated Fermi-Pasta-Ulam (F P U ) chain completely alters the thermal transport characteristics. The resulting F P U C chains, while being momentum preserving, satisfy the Fourier's law and do not show anomalous thermal transport behavior. Collisions play a significant role in reducing the boundary jumps typically observed in F P U chains. The thermal conductivity of the F P U C chains is significantly smaller than the F P U chains at low temperatures due to the fast redistribution of energy from the lowest mode of vibrations to the higher modes. At high temperatures, however, the F P U C chains have larger thermal conductivity than the F P U chains due to the large contributions to the heat flux because of the large-magnitude short-ranged anharmonic collision force.