Distributed quantum entanglement plays a crucial role in realizing networks that connect quantum devices. However, sharing entanglement between distant nodes by means of photons is a challenging process primary due to unavoidable losses in the linking channels. In this paper, we propose a simple loss-tolerant protocol for the Greenberger-Horne-Zeilinger-state distribution. We analyze the distribution rate under feasible experimental conditions and demonstrate the advantages of rate-loss scaling with respect to direct transmission. Our protocol does not use quantum repeaters and is achievable with current quantum optics technology. The result has direct application to tasks such as conference key agreement or distributed sensing. Moreover, it reduces the requirements for implementing distributed quantum error correction codes such as the surface code.