  Chandra and XMM-Newton have resolved the 2-8 keV X-ray Background (XRB) into
point sources. Many of the fainter sources are obscured active galactic nuclei
(AGN) with column densities in the range of 10^22-10^23 pcmsq, some of which
have quasar-like luminosities. According to obscuration models, the XRB above 8
keV is dominated by emission from Compton-thick AGN, with column densities
exceeding 1.5 times 10^24 pcmsq. Here, we consider whether Compton-thick
quasars are detectable by Chandra and XMM-Newton by their direct (i.e. not
scattered) X-ray emission. Detectability is optimized if the objects
individually have a high luminosity and high redshift, so that the direct
emission has a significant flux in the observed band. Using a simple galaxy
formation model incorporating accreting black holes, in which quasars build
most of their mass in a Compton-thick manner before expelling the obscuring
matter, we predict that moderately deep 100 ks Chandra and XMM-Newton exposures
may contain a handful of detectable Compton-thick quasars. Deep Ms or more
Chandra images should contain 50-100 distant, optically-faint, Compton-thick
sources. In passing we show that radiation pressure can be as effective in
expelling the obscuring gas as quasars winds, and yields a black hole mass
proportional to the velocity dispersion of the host bulge to the fourth power.
