  The precision of intensity measurements of the extragalactic X-ray Background
(XRB) on an angular scale of about a degree is dominated by spatial
fluctuations caused by source confusion noise. X-ray source counts at the flux
level responsible for these fluctuations will soon be accurately measured by
new missions and it will then be possible to detect the weaker fluctuations
caused by the clustering of the fainter, more distant sources which produce the
bulk of the XRB. We show here that measurements of these excess fluctuations at
the level of 0.2 per cent are within reach, improving by an order of magnitude
on present upper limits. Together with the redshift evolution of the X-ray
volume emissivity in the Universe, this can be used to measure the power
spectrum of the density fluctuations at comoving wavevectors 0.01-0.1 h/Mpc at
z=1-2 with a sensitivity better than the predictions from large-scale structure
models. A relatively simple X-ray experiment, carried out by a large-area
proportional counter with a 0.5-2 deg^2 collimated field-of-view scanning the
whole sky a few times, would be able to determine the power spectrum of the
density fluctuations near its expected peak in wavevector with an accuracy
better than 10 per cent.
