  We show numerically that including soft-sphere type collisions in the
celebrated Fermi-Pasta-Ulam ($FPU$) chain completely alters the thermal
transport characteristics. The resulting $FPU^C$ 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 $FPU$ chains. The thermal conductivity of the
$FPU^C$ chains is significantly smaller than the $FPU$ 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 $FPU^C$
chains have larger thermal conductivity than the $FPU$ chains due to the large
contributions to the heat flux because of the large-magnitude short-ranged
anharmonic collision force.
