  Individually addressed Er$^{3+}$ ions in solid-state hosts are promising
resources for quantum repeaters, because of their direct emission in the
telecom band and compatibility with silicon photonic devices. While the
Er$^{3+}$ electron spin provides a spin-photon interface, ancilla nuclear spins
could enable multi-qubit registers with longer storage times. In this work, we
demonstrate coherent coupling between the electron spin of a single Er$^{3+}$
ion and a single $I=1/2$ nuclear spin in the solid-state host crystal, which is
a fortuitously located proton ($^1$H). We control the nuclear spin using
dynamical decoupling sequences applied to the electron spin, implementing one-
and two-qubit gate operations. Crucially, the nuclear spin coherence time
exceeds the electron coherence time by several orders of magnitude, because of
its smaller magnetic moment. These results provide a path towards combining
long-lived nuclear spin quantum registers with telecom-wavelength emitters for
long-distance quantum repeaters.
