  A heavy hole confined to an InGaAs quantum dot promises the union of a stable
spin and optical coherence to form a near perfect, high-bandwidth spin-photon
interface. Despite theoretical predictions and encouraging preliminary
measurements, the dynamic processes determining the coherence of the hole spin
are yet to be understood. Here, we establish the regimes that allow for a
highly coherent hole spin in these systems, recovering a crossover from
hyperfine to electrical-noise dominated decoherence with a few-Tesla external
magnetic field. Dynamical decoupling allows us to reach the longest
ground-state coherence time, T2, of 4.4 $\mu$s, observed in this system. The
improvement of coherence we measure is quantitatively supported by an
independent analysis of the local electrical environment.
