  Cavity electromechanics relies on parametric coupling between microwave and
mechanical modes to manipulate the mechanical quantum state, and provide a
coherent interface between different parts of hybrid quantum systems. High
coherence of the mechanical mode is of key importance in such applications, in
order to protect the quantum states it hosts from thermal decoherence. Here, we
introduce an electromechanical system based around a soft-clamped mechanical
resonator with an extremely high Q-factor (>$10^9$) held at very low (30 mK)
temperatures. This ultracoherent mechanical resonator is capacitively coupled
to a microwave mode, strong enough to enable ground-state-cooling of the
mechanics ($\bar{n}_\mathrm{min}= 0.76\pm 0.16$). This paves the way towards
exploiting the extremely long coherence times ($t_\mathrm{coh}>100 ms) offered
by such systems for quantum information processing and state conversion.
