Can X-rays provide a solution to the abundance discrepancy problem in
  photoionised nebulae?
  We re-examine the well-known discrepancy between ionic abundances determined
via the analysis of recombination lines (RLs) and collisionally excited lines
(CELs). We show that abundance variations can be mimicked in a {\it chemically
homogeneous} medium by the presence of dense X-ray irradiated regions which
present different ionisation and temperature structures from those of the more
diffuse medium they are embedded in, which is predominantly ionised by
extreme-ultraviolet radiation. The presence of X-ray ionised dense clumps or
filaments also naturally explains the lower temperatures often measured from O
{\sc ii} recombination lines and from the Balmer jump when compared to
temperatures determined by CELs. We discuss the implications for abundances
determined via the analysis of CELs and RLs and provide a simple analytical
procedure to obtain upwards corrections for CEL-determined abundance. While we
show that the abundance discrepancy factor (ADF) and the Balmer Jump
temperature determined from observations of the Orion Nebula can simultaneously
be reproduced by this model (implying upward corrections for CELs by a factor
of 1.15), we find that the required X-ray fluxes exceed the known Orion's
stellar and diffuse X-ray budget, if we assume that the clumps are located at
the edge of the blister. We propose, however, that spatially resolved
observations may be used to empirically test the model, and we outline how the
framework developed in this letter may be applied in the future to objects with
better constrained geometries (e.g. planetary nebulae).
