  We study the influence of external electric, $E$, and magnetic, $B$, fields
parallel to each other, and of a chiral chemical potential, $\mu_5$, on the
chiral phase transition of Quantum Chromodynamics. Our theoretical framework is
a Nambu-Jona-Lasinio model with a contact interaction. Within this model we
compute the critical temperature of chiral symmetry restoration, $T_c$, as a
function of the chiral chemical potential and field strengths. We find that the
fields inhibit and $\mu_5$ enhances chiral symmetry breaking, in agreement with
previous studies.
