  Cross sections for the rotational (de)excitation of CO by ground state para-
and ortho-H_2 are obtained using quantum scattering calculations for collision
energies between 1 and 520 cm^{-1}. A new CO-H_2 potential energy surface is
employed and its quality is assessed by comparison with explicitly correlated
CCSD(T)-R12 calculations. Rate constants for rotational levels of CO up to 5
and temperatures in the range 5-70 K are deduced. The new potential is found to
have a strong influence on the resonance structure of the cross sections at
very low collision energies. As a result, the present rates at 10 K differ by
up to 50% with those obtained by \citet{flower01} on a previous, less accurate,
potential energy surface.
