  Erbium ions doped into crystals have unique properties for quantum
information processing, because of their optical transition at 1.5 $\mu$m and
of the large magnetic moment of their effective spin-1/2 electronic ground
state. Most applications of erbium require however long electron spin coherence
times, and this has so far been missing. Here, by selecting a host matrix with
a low nuclear-spin density (CaWO$_4$) and by quenching the spectral diffusion
due to residual paramagnetic impurities at millikelvin temperatures, we obtain
an Er$^{3+}$ electron spin coherence time of 23 ms. This is the longest
electron spin coherence time measured in a material with a natural abundance of
nuclear spins and on a magnetically-sensitive transition. Our results establish
Er$^{3+}$:CaWO$_4$ as a leading platform for quantum networks.
