Quantum computation requires qubits that satisfy often-conflicting criteria, which include long-lasting coherence and scalable control1. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits. Although such encoded qubits may be particularly susceptible to leakage out of their computational subspace, they can be insensitive to certain noise processes2,3 and can also allow logical control with a single type of entangling interaction4 while maintaining favourable features of the underlying physical system. Here we demonstrate high-fidelity operation of an exchange-only qubit encoded in a subsystem of three coupled electron spins5 confined in gated, isotopically enhanced silicon quantum dots6. This encoding requires neither high-frequency electric nor magnetic fields for control, and instead relies exclusively on the exchange interaction4,5, which is highly local and can be modulated with a large on-off ratio using only fast voltage pulses. It is also compatible with very low and gradient-free magnetic field environments, which simplifies integration with superconducting materials. We developed and employed a modified blind randomized benchmarking protocol that determines both computational and leakage errors7,8, and found that unitary operations have an average total error of 0.35%, with half of that, 0.17%, coming from leakage driven by interactions with substrate nuclear spins. The combination of this proven performance with complete control via gate voltages makes the exchange-only qubit especially attractive for use in many-qubit systems.