  We investigate the magneto-optical properties of excitons bound to single
stacking faults in high-purity GaAs. We find that the two-dimensional stacking
fault potential binds an exciton composed of an electron and a heavy-hole, and
confirm a vanishing in-plane hole $g$-factor, consistent with the atomic-scale
symmetry of the system. The unprecedented homogeneity of the stacking-fault
potential leads to ultra-narrow photoluminescence emission lines (with
full-width at half maximum ${\lesssim 80~\mu \text{eV} }$) and reveals a large
magnetic non-reciprocity effect that originates from the magneto-Stark effect
for mobile excitons. These measurements unambiguously determine the direction
and magnitude of the giant electric dipole moment (${\gtrsim e \cdot
10~\text{nm}}$) of the stacking-fault exciton, making stacking faults a
promising new platform to study interacting excitonic gases.
