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.
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