  This Letter reports the observation of $WZ\gamma$ production and a
measurement of its cross-section using 140.1 $\pm$ 1.2 fb$^{-1}$ of
proton-proton collision data recorded at a center-of-mass energy of 13 TeV by
the ATLAS detector at the Large Hadron Collider. The $WZ\gamma$ production
cross-section, with both the $W$ and $Z$ bosons decaying leptonically, $pp
\rightarrow WZ\gamma \rightarrow {\ell'}^{\pm}\nu\ell^{+}\ell^{-}\gamma$
($\ell^{(')} = e, \mu$), is measured in a fiducial phase-space region defined
such that the leptons and the photon have high transverse momentum and the
photon is isolated. The cross-section is found to be 2.01 $\pm$ 0.30 (stat.)
$\pm$ 0.16 (syst) fb. The corresponding Standard Model predicted cross-section
calculated at next-to-leading order in perturbative quantum chromodynamics and
at leading order in the electroweak coupling constant is 1.50 $\pm$ 0.06 fb.
The observed significance of the $WZ\gamma$ signal is 6.3$\sigma$, compared
with an expected significance of 5.0$\sigma$.
