  We study the gauge dependence of the quark propagator in quantum
chromodynamics by solving the gap equation with a nonperturbative quark-gluon
vertex which is constrained by longitudinal and transverse Slavnov-Taylor
identities, the discrete charge conjugation and parity symmetries and which is
free of kinematic singularities in the limit of equal incoming and outgoing
quark momenta. We employ gluon propagators in renormalizable $R_\xi$ gauges
obtained in lattice QCD studies. We report the dependence of the
nonperturbative quark propagator on the gauge parameter, in particular we
observe an increase, proportional to the gauge-fixing parameter, of the mass
function in the infrared domain, whereas the wave renormalization decreases
within the range $0 \leq \xi \leq 1$ considered here. The chiral quark
condensate reveals a mild gauge dependence in the region of $\xi$ investigated.
We comment on how to build and improve upon this exploratory study in future in
conjunction with generalized gauge covariance relations for QCD.
