Cavity quantum electrodynamics, which explores strong light-matter interaction at the single-photon level, has provided a foundation for work to study, manipulate, and build systems managing quantum states. A parallel site of richness has been the study of topology in condensed matter physics; beyond its intrinsic value, the robustness to disorder afforded by topological structure, sometimes generated via a time-reversal-symmetry-breaking gauge field as in the case of the quantum Hall effect, has become of interest as a route to protection of quantum excitations. In this thesis, we mix these two regimes, exploring cavity quantum electrodynamics in a topological metamaterial which breaks time-reversal symmetry for microwave photons by realizing a synthetic gauge field ‘felt’ by these photons. We strongly couple the edge of this quarter-flux Harper-Hofstadter lattice, a 2D array of coupled superconducting cavity resonators, to a single transmon qubit, demonstrating Rabi oscillations between the excited transmon and each individual mode of the topological band structure and profiling the multimode Lamb shift on the qubit from the forest of the synthetic vacuum. Then, inspired by recent efforts to achieve chiral emission and transport of photons for use in quantum information science, we introduce a second transmon qubit to another site along the lattice edge and use this to detect a single photon confined to propagate in the chiral edge of this topological photonic bulk. This demonstration of nonreciprocal transport between quantum emitters coupled to an engineered chiral channel offers opportunities to build and probe entangled states of light which gain structure from the system topology, and is a step along the path to exploring topological quantum matter.