  We calculate at two-loop order in chiral perturbation theory the
electromagnetic corrections to the dominant two-pion exchange nucleon-nucleon
interaction that is generated by the isoscalar $\pi N$ contact-vertex
proportional to the large low-energy constant $c_3$. We find that the
respective $2\pi\gamma$-exchange potential contains sizeable isospin-breaking
components which amount to about -1% of the strongly attractive isoscalar
central $2\pi$-exchange potential. The typical value of these novel
charge-independence and charge-symmetry breaking central potentials is $0.3
$MeV at a nucleon distance of $r= m_\pi^{-1} = 1.4 $fm. Our analytical result
for this presumably dominant $2\pi\gamma$-exchange interaction is in a form
such that it can be easily implemented into phase-shift analyses and few-body
calculations.
