  We demonstrate a two-qubit logic gate driven by near-field microwaves in a
room-temperature microfabricated ion trap. We measure a gate fidelity of
99.7(1)\%, which is above the minimum threshold required for fault-tolerant
quantum computing. The gate is applied directly to $^{43}$Ca$^+$ "atomic clock"
qubits (coherence time $T_2^*\approx 50\,\mathrm{s}$) using the microwave
magnetic field gradient produced by a trap electrode. We introduce a
dynamically-decoupled gate method, which stabilizes the qubits against
fluctuating a.c.\ Zeeman shifts and avoids the need to null the microwave
field.
