  We present a cross-correlation analysis to constrain the faint galaxy
contribution to the cosmic X-ray background (XRB). Cross-correlating faint
optical galaxy catalogues with unidentified X-ray sources from 3 deep ROSAT
fields we find that B < 23 galaxies account for 20+-7 % of all X-ray sources to
a flux limit of S(0.5-2.0 keV)=4x10^{-15} erg s-1 cm-2. To probe deeper,
galaxies are then cross-correlated with the remaining unresolved X-ray images.
A highly significant signal is obtained on each field. Allowing for the effect
of the ROSAT point-spread function, and deconvolving the effect of galaxy
clustering, we find that faint B < 23 galaxies directly account for 23+-3% of
the unresolved XRB at 1keV. Using the optical magnitude of faint galaxies as
probes of their redshift distribution, we find evidence for strong evolution in
their X-ray luminosity, parameterised with the form L_x \propto (1+z)^3.2+-1.0.
Extrapolation to z=2 will account for 40+-10% of the total XRB at 1keV. The
nature of the emitting mechanism in these galaxies remains unclear, but we
argue that obscured and/or low luminosity AGN provide the most natural
explanation.
