  We present a holographic model of QCD with a first order chiral restoration
phase transition with chemical potential, mu. The first order behaviour follows
from allowing a discontinuity in the dual description as the quarks are
integrated out below their constituent mass. The model predicts a deconfined
yet massive quark phase at intermediate densities (350 MeV< mu <500 MeV), above
the nuclear density phase, which has a very stiff equation of state and a speed
of sound close to one. We also include a holographic description of a colour
superconducting condensate in the chirally restored vacuum and study the
resulting equation of state. They provides a well behaved first order
transition from the deconfined massive quark phase at very high density (mu>500
MeV). We solve the Tolman-Oppenheimer-Volkoff equations with the resulting
equations of state and find stable hybrid stars with quark cores. We compute
the tidal deformability for these hybrid stars and show they are consistent
with LIGO/Virgo data on a neutron star collision. Our holographic model shows
that quark matter could be present at the core of such compact stars.
