We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated surface ion trap. We introduce a dynamically decoupled gate method, which stabilizes the qubits against fluctuating energy shifts and avoids the need to null the microwave field. We use the gate to produce a Bell state with fidelity 99.7(1)%, after accounting for state preparation and measurement errors. The gate is applied directly to ⁴³Ca+ hyperfine “atomic clock” qubits (coherence time T∗2≈50  s) using the oscillating magnetic field gradient produced by an integrated microwave electrode.