  We calculate the chiral condensate in neutron matter at zero temperature
based on nuclear forces derived within chiral effective field theory. Two-,
three- and four-nucleon interactions are included consistently to
next-to-next-to-next-to-leading order (N3LO) of the chiral expansion. We find
that the interaction contributions lead to a modest increase of the condensate,
thus impeding the restoration of chiral symmetry in dense matter and making a
chiral phase transition in neutron-rich matter unlikely for densities that are
not significantly higher than nuclear saturation density.
