  We perform a relativistic chiral effective field theory calculation of the
radiative pion photoproduction ($\gamma p \to \pi^0 p \gamma'$) in the
$\Delta$-resonance region, to next-to-leading order in the ``delta-expansion''.
This work is aimed at a model-independent extraction of the $\Delta^+$ magnetic
moment from new precise measurements of this reaction. It also predicts the
chiral behavior of $\Delta$'s magnetic moment, which can be used to extrapolate
the recent lattice QCD results to the physical point.
