Reaching the quantum limit for added noise in amplification processes is an important step toward many quantum technologies. Nearly quantum-limited traveling-wave parametric amplifiers with Josephson junction arrays have been developed and recently even become commercially available. However, the fundamental question of whether a single atom also can reach this quantum limit has not yet been answered in practice. Here, we investigate the amplification of a microwave probe signal by a superconducting artificial atom, a transmon, at the end of a semi-infinite transmission line, under a strong pump field. The end of the transmission line acts as a mirror for microwave fields. Due to the weak anharmonicity of the artificial atom, the strong pump field creates multi-photon excitations among the dressed states. Transitions between these dressed states, Rabi sidebands, give rise to either amplification or attenuation of the weak probe. We obtain a maximum power amplification of 1.402 ± 0.025, higher than in any previous experiment with a single artificial atom. We achieve near-quantum-limited added noise (0.157 ± 0.003 quanta; the quantum limit is 0.143 ± 0.006 quanta for this level of amplification), due to quantum coherence between Rabi sidebands, leading to constructive interference between emitted photons.