  We calculate the one-photon loop radiative corrections to the charged
pion-pair production process $\pi^-\gamma\to\pi^+\pi^-\pi^-$. In the low-energy
region this reaction is governed by the chiral pion-pion interaction. The
pertinent set of 42 irreducible photon-loop diagrams is calculated by using the
package FeynCalc. Electromagnetic counterterms with two independent low-energy
constants $\widehat k_1$ and $\widehat k_2$ are included in order to remove the
ultraviolet divergences generated by the photon-loops. Infrared finiteness of
the virtual radiative corrections is achieved by including soft photon
radiation below an energy cut-off $\lambda$. The purely electromagnetic
interaction of the charged pions mediated by one-photon exchange is also taken
into account. The radiative corrections to the total cross section (in the
isospin limit) vary between $+10\%$ close to threshold and about $-1\%$ at a
center-of-mass energy of $7m_\pi$. The largest contribution comes from the
simple one-photon exchange. Radiative corrections to the $\pi^+\pi^-$ and
$\pi^-\pi^-$ mass spectra are studied as well. The Coulomb singularity of the
final-state interaction produces a kink in the dipion mass spectra. The virtual
radiative corrections to elastic $\pi^-\pi^-$ scattering are derived
additionally.
