Chiral nanophotonic components, such as waveguides and resonators coupled to quantum emitters, provide a fundamentally new approach to manipulate light-matter interactions. The recent emergence of topological photonics has provided a new paradigm to realize helical/chiral nanophotonic structures that are flexible in design and, at the same time, robust against sharp bends and disorder. Here we demonstrate such a topologically protected chiral nanophotonic resonator that is strongly coupled to a solid-state quantum emitter. Specifically, we employ the valley-Hall effect in a photonic crystal to achieve topological edge states at an interface between two topologically distinct regions. Our helical resonator supports two counterpropagating edge modes with opposite polarizations. We first show chiral coupling between the topological resonator and the quantum emitter such that the emitter emits preferably into one of the counterpropagating edge modes depending upon its spin. Subsequently, we demonstrate strong coupling between the resonator and the quantum emitter using resonant Purcell enhancement in the emission intensity by a factor of 3.4. Such chiral resonators could enable designing complex nanophotonic circuits for quantum information processing and studying novel quantum many-body dynamics.