  We critique the hypothesis that the first stars were very massive stars (VMS;
M > 140 Msun). We review the two major lines of evidence for the existence of
VMS: (1) that the relative metal abundances of extremely metal-poor Galactic
halo stars show evidence of VMS enrichment, and (2) that the high
electron-scattering optical depth (tau_e) to the CMB found by WMAP requires VMS
for reionization in a concordance LambdaCDM cosmology. The supernova yield
patterns of VMS are incompatible with the Fe-peak and r-process abundances in
halo stars. Models including Type II supernovae and/or ``hypernovae'' from
metal-free progenitors with 8 - 40 Msun can better explain the observed trends.
With a simple metal-transport model, we estimate that halo enrichment curtails
metal-free star formation after ~10^8 yr at z ~ 20. Because the ionizing photon
efficiency of metal-free stars peaks at ~120 Msun and declines at higher mass,
an IMF with a lower bound at M ~ 10 - 20 Msun and no VMS can maximize the
ionizing photon budget and still be consistent with the nucleosynthetic
evidence. An IMF devoid of low-mass stars is justified independently by models
of the formation of primordial stars. Using a semi-analytic model for H I and
He II reionization, we find that such an IMF can reproduce tau_e = 0.10 - 0.14,
consistent with the range from WMAP. We conclude, on the basis of these
results, that VMS are not necessary to meet the existing constraints commonly
taken to motivate them.
