  The charge asymmetry in the differential cross section of high-energy
$\mu^+\mu^-$ photoproduction in the electric field of a heavy atom is obtained.
This asymmetry arises due to the Coulomb corrections to the amplitude of the
process (next-to-leading term with respect to the atomic field). The deviation
of the nuclear electric field from the Coulomb field at small distances is
crucially important for the charge asymmetry. Though the Coulomb corrections to
the total cross section are negligibly small, the charge asymmetry is
measurable for selected final states of $\mu^+$ and $\mu^-$. We further discuss
the feasibility for experimental observation of this effect.
