  The cross section of a top-quark pair produced in association with a photon
is measured in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}
= 8$ TeV with $20.2$ fb$^{-1}$ of data collected by the ATLAS detector at the
Large Hadron Collider in 2012. The measurement is performed by selecting events
that contain a photon with transverse momentum $p_\mathrm{T} > 15$ GeV, an
isolated lepton with large transverse momentum, large missing transverse
momentum, and at least four jets, where at least one is identified as
originating from a $b$-quark. The production cross section is measured in a
fiducial region close to the selection requirements. It is found to be $139 \pm
7 (\mathrm{stat.}) \pm 17 (\mathrm{syst.})$ fb, in good agreement with the
theoretical prediction at next-to-leading order of $151 \pm 24$ fb. In
addition, differential cross sections in the fiducial region are measured as a
function of the transverse momentum and pseudorapidity of the photon.
