In this paper, we propose a massive MIMO (multiple-input-multiple-output) architecture with distributed steerable phased antenna subarrays for position estimation in the mmWave range. We also propose localization algorithms and a multistage/multiresolution search strategy that resolve the problem of high side lobes, which is inherent in spatially coherent localization. The proposed system is intended for use in line-of-sight indoor environments. Time synchronization between the transmitter and the receiving system is not required, and the algorithms can also be applied to a multiuser scenario. The simulation results for the line-of-sight-only and specular multipath scenarios show that the localization error is only a small fraction of the carrier wavelength and that it can be achieved under reasonable system parameters including signal-to-noise ratios, antenna number/placement, and subarray apertures. The proposed concept has the potential of significantly improving the capacity and spectral/energy efficiency of future mmWave massive MIMO systems.