  We place firm upper limits on the global accretion history of massive black
holes at z>5 from the recently measured unresolved fraction of the cosmic X-ray
background. The maximum allowed unresolved intensity observed at 1.5 keV
implies a maximum accreted-mass density onto massive black holes of rho_acc <
1.4E4 M_sun Mpc^{-3} for z>5. Considering the contribution of lower-z AGNs, the
value reduces to rho_acc < 0.66E4 M_sun Mpc^{-3}. The tension between the need
for the efficient and rapid accretion required by the observation of massive
black holes already in place at z>7 and the strict upper limit on the accreted
mass derived from the X-ray background may indicate that black holes are rare
in high redshift galaxies, or that accretion is efficient only for black holes
hosted by rare galaxies.
