  Some years ago Gribov developed the so-called supercritical light quark
confinement scenario. Based on physical arguments he conjectured a drastic
change in the analytical properties of the quark propagator when the
back-reaction of Goldstone bosons (pions) is considered. We investigate this
scenario and provide numerical solutions for the quark propagator in the
complex plane with and without the pion back-reaction. We find no evidence for
the scenario Gribov advocated. As an aside we present a novel method to solve
the quark Dyson-Schwinger equation in the complex plane and discuss new
characteristics of dynamical chiral symmetry breaking in our truncation scheme.
