  This report describes the conceptual design of a $\gamma\gamma$ Higgs factory
in which 62.8 GeV electron beams collide with 1 keV X-ray free electron laser
(XFEL) beams to produce colliding beams of 62.5 GeV photons. The Higgs boson
production rate is 80,000 Higgs bosons per 10$^7$ second year, roughly the same
as the ILC Higgs rate at $\sqrt{s}$=250 GeV. The electron accelerator is based
on cold copper distributed coupling (C$^3$) accelerator technology. Unlike the
center-of-mass energy spectra of previous optical wavelength $\gamma\gamma$
collider designs, the sharply peaked $\gamma\gamma$ center-of-mass energy
spectrum of XCC produces model independent Higgs coupling measurements with
precision on par with $e^+e^-$ colliders. For the triple Higgs coupling
measurement, the XCC center-of-mass energy can be upgraded to 380 GeV, where
the cross section for $\gamma\gamma\rightarrow HH$ is twice that of $e^+e^-
\rightarrow ZHH$ at $\sqrt{s}$=500 GeV. Design challenges are discussed, along
with the R\&D to address them, including demonstrators.
