Millimeter wave (mmWave) multiple-input multipleoutput (MIMO) communication with large antenna arrays has been proposed to enable gigabit per second communication for next generation cellular systems and local area networks. A key difference relative to lower frequency solutions is that in mmWave systems, precoding/combining can not be performed entirely at digital baseband, due to the high cost and power consumption of some components of the radio frequency (RF) chain. In this paper we develop a low complexity algorithm for finding hybrid precoders that split the precoding/combining process between the analog and digital domains. Our approach exploits sparsity in the received signal to formulate the design of the precoder/combiners as a compressed sensing optimization problem. We use the properties of the matrix containing the array response vectors to find first an orthonormal analog precoder, since sparse approximation algorithms applied to orthonormal sensing matrices are based on simple computations of correlations. Then, we propose to perform a local search to refine the analog precoder and compute the baseband precoder. We present numerical results demonstrate substantial improvements in complexity while maintaining good spectral efficiency.