Measurement of the state of a quantum system with inherent quantum uncertainty (noise) approaching the ultimate physical limits is of both technological and fundamental interest. Quantum noise prevents any mutually nonorthogonal quantum states, such as coherent states, from being distinguished with perfect accuracy. Optimized quantum measurements for nonorthogonal coherent states allow, in principle, for state discrimination sensitivities surpassing the standard quantum limit. Realizing quantum receivers that can detect multiple coherent states with sensitivity levels approaching the ultimate quantum limits is fundamental to quantum-enhanced measurements, and can optimize the performance of quantum and classical communications as well as future implementations of quantum technologies. Here, we demonstrate the first quantum receiver that unconditionally discriminates four nonorthogonal coherent states with error probabilities below the standard quantum limit. This receiver achieves error rates four times lower than is possible with any ideal conventional receiver with perfect detection efficiency.