  Primordial star formation appears to result in stars at least an order of
magnitude more massive than modern star formation. It has been proposed that
the transition from primordial to modern initial mass functions occurs due to
the onset of effective metal line cooling at a metallicity Z/Z_sun = 10^{-3.5}.
However, these simulations neglected molecular hydrogen cooling. We perform
simulations using the same initial conditions, but including molecular cooling,
using a complex network that follows molecular hydrogen formation and also
directly follows carbon monoxide and water. We find that molecular hydrogen
cooling allows roughly equivalent fragmentation to proceed even at zero
metallicity for these initial conditions. The apparent transition just
represents the point where metal line cooling becomes more important than
molecular cooling. In all cases, the fragments are massive enough to be
consistent with models of primordial stellar masses, suggesting that the
transition to the modern initial mass function may be determined by other
physics such as dust formation. We conclude that such additional cooling
mechanisms, combined with the exact initial conditions produced by cosmological
collapse are likely more important than metal line cooling in determining the
initial mass function, and thus that there is unlikely to be a sharp transition
in the initial mass function at Z/Z_sun = 10^{-3.5}.
