  We suggest the idea, supported by concrete calculations within chiral models,
that the critical endpoint of the phase diagram of Quantum Chromodynamics with
three colors can be detected, by means of Lattice simulations of
grand-canonical ensembles with a chiral chemical potential, $\mu_5$, conjugated
to chiral charge density. In fact, we show that a continuation of the critical
endpoint of the phase diagram of Quantum Chromodynamics at finite chemical
potential, $\mu$, to a critical end point in the temperature-chiral chemical
potential plane, is possible. This study paves the way of the mapping of the
phases of Quantum Chromodynamics at finite $\mu$, by means of the phases of a
fictitious theory in which $\mu$ is replaced by $\mu_5$.
