  High-order harmonic generation (HHG) in simultaneous intense near-infrared
(NIR) laser light and brilliant x rays above an inner-shell absorption edge is
examined. A tightly bound inner-shell electron is transferred into the
continuum. Then, NIR light takes over and drives the liberated electron through
the continuum until it eventually returns to the cation leading in some cases
to recombination and emission of a high-order harmonic (HH) photon that is
upshifted by the x-ray photon energy. We develop a theory of this scenario and
apply it to $1s$ electrons of neon atoms. The boosted HH light is used to
generate a single attosecond pulse in the kiloelectronvolt regime. Prospects
for nonlinear x-ray physics and HHG-based spectroscopy involving core orbitals
are discussed.
