The negatively-charged silicon-vacancy (SiV$^-$) color center in diamond has recently emerged as a promising system for quantum photonics. Its symmetry-protected optical transitions enable creation of indistinguishable emitter arrays and deterministic coupling to nanophotonic devices. Despite this, the longest coherence time associated with its electronic spin achieved to date ($sim 250$ ns) has been limited by coupling to acoustic phonons. We demonstrate coherent control and suppression of phonon-induced dephasing of the SiV$^-$ electronic spin coherence by five orders of magnitude by operating at temperatures below 500 mK. By aligning the magnetic field along the SiV$^-$ symmetry axis, we demonstrate spin-conserving optical transitions and single-shot readout of the SiV$^-$ spin with 89% fidelity. Coherent control of the SiV$^-$ spin with microwave fields is used to demonstrate a spin coherence time $T_2$ of 13 ms and a spin relaxation time $T_1$ exceeding 1 s at 100 mK. These results establish the SiV$^-$ as a promising solid-state candidate for the realization of scalable quantum networks.
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