Classical beamforming techniques rely on highly linear transmitters and receivers to allow phase-coherent combining at the transmitter and receiver. The transmitter uses beamforming to steer signal power towards the receiver, and the receiver uses beamforming to gather and coherently combine the signals from multiple receiver antennas. When the transmitters and receivers are instead constrained for power and cost reasons to be non-linear one-bit devices, the potential advantages and performance metrics associated with beamforming are not as well understood. We define beamforming at the transmitter as a codebook design problem to maximize the minimum distance between codewords. We define beamforming at the receiver as the maximum likelihood detector of the transmitted codeword. We show that beamforming with one-bit transceivers is a constellation design problem, and that we can come within a few dB SNR of the capacity attained by linear transceivers.