Stable sources of entangled photons are important requirements for quantum communications. In recent years, cascaded downconversion has been demonstrated as an effective method of directly producing three-photon entanglement. However, to produce polarization entanglement these sources have until now relied on intricate active phase stabilization schemes, thus limiting their robustness and usability. In this work, we present a completely phase-stable source of three-photon entanglement in the polarization degree of freedom. With this source, which is based on a cascade of two pair sources based on Sagnac configurations, we produce states with over 96% fidelity with an ideal GHZ state. Moreover, we demonstrate the stability of the source over several days without any ongoing optimization. We expect this source to be a useful tool for applications requiring multiphoton entanglement, such as quantum secret sharing and producing heralded entangled photon pairs.