  Generating large multiphoton entangled states is of main interest due to
enabling universal photonic quantum computing and all-optical quantum repeater
nodes. These applications exploit measurement-based quantum computation using
cluster states. Remarkably, it was shown that photonic cluster states of
arbitrary size can be generated by using feasible heralded linear optics fusion
gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ)
states as the initial resource state. Thus, the capability of generating
heralded GHZ states is of great importance for scaling up photonic quantum
computing. Here, we experimentally demonstrate this required building block by
reporting a polarisation-encoded heralded GHZ state of three photons, for which
we build a high-rate six-photon source ($547{\pm}2$ Hz) from a solid-state
quantum emitter and a stable polarisation-based interferometer. The detection
of three ancillary photons heralds the generation of three-photon GHZ states
among the remaining particles with fidelities up to
$\mathcal{F}=0.7278{\pm}0.0106$. Our results initiate a path for scalable
entangling operations using heralded linear-optics implementations.
