Amplifiers are crucial in every experiment carrying out a very sensitive measurement. However, they always degrade the information by adding noise. Quantum mechanics puts a limit on how small this degradation can be. Theoretically, the minimum noise energy added by a phase-preserving amplifier to the signal it processes amounts at least to half a photon at the signal frequency. In this article, we show that we can build a practical microwave amplifying circuit that fulfills the minimal requirements to reach this quantum limit. The readout of solid-state qubits, and more generally, the measurement of very weak signals in various areas of science, can benefit from this new superconducting device. We also discuss how our circuit can be the basic buiding block for a variety of practical applications such as frequency conversion with and without photon number gain, dynamic cooling and production of entangled signal pairs.