  We present three-loop helicity amplitudes for the production of a single
photon in association with one jet in Quantum Chromodynamics, a final state
which provides a standard candle of the Standard Model at the Large Hadron
Collider. We employ a recently-proposed variation of the so-called tensor
projection method in the 't Hooft-Veltman scheme (tHV) which avoids the
computation of contributions due to unphysical (-2$\epsilon$)-dimensional
polarisations of the external states. We obtain compact analytic results
expressed in terms of harmonic polylogarithms.
