  We combine Lyman-break colour selection with ultradeep (> 200 ks) Chandra
X-ray imaging over a survey area of ~0.35 deg^2 to select high redshift AGN.
Applying careful corrections for both the optical and X-ray selection
functions, the data allow us to make the most accurate determination to date of
the faint end of the X-ray luminosity function (XLF) at z~3. Our methodology
recovers a number density of X-ray sources at this redshift which is at least
as high as previous surveys, demonstrating that it is an effective way of
selecting high z AGN. Comparing to results at z=1, we find no evidence that the
faint slope of the XLF flattens at high z, but we do find significant (factor
~3.6) negative evolution of the space density of low luminosity AGN. Combining
with bright end data from very wide surveys we also see marginal evidence for
continued positive evolution of the characteristic break luminosity L*. Our
data therefore support models of luminosity-dependent density evolution between
z=1 and z=3. A sharp upturn in the the XLF is seen at the very lowest
luminosities (Lx < 10^42.5 erg s^-1), most likely due to the contribution of
pure X-ray starburst galaxies at very faint fluxes.
