Analytic arguments have suggested that the existence of high-redshift
quasars challenges hierarchical galaxy formation theories in which the
majority of galaxies form late. We address this issue by using a seri
es of numerical simulations of the biased cold dark matter model with
and without gas dynamics. Potential quasar sites are identified with m
assive density peaks collapsing to form massive self-gravitating cold,
gas clouds. The Press-Schechter formalism, using a Gaussian filter wi
th delta(c) = 1.61, correctly predicts the number of high-mass dark ha
loes. Very efficient cooling and angular momentum transfer to the dark
halo, however, allow the gas to become much denser than naive predict
ions would suggest. We find that there are > 10(3) times the required
number of potential quasar sites at z = 4.5; at z = 8 there is already
at least one site in our simulation volume of 10(6) Mpc(3). Thus site
s for quasars could easily form at significantly higher redshifts than
those of observed quasars, even in models where most galaxy formation
occurs late.