In this paper, polar codes are first applied in non-orthogonal multiple access (NOMA) and the channel polarization idea is extended to NOMA, which is a major multiple access technique in 5G systems. The polar coded NOMA (PC-NOMA) scheme is proposed, whereby the NOMA channel is decomposed into a series of binary-input channels under a two-stage channel polarization transform. In the first stage, the NOMA channel is divided into a group of user synthesized channels by using the multi-level coding structure. In the second stage, based on the structure of bit-interleaved code modulation, user synthesized channels are further decomposed into binary polarized channels. Then, a joint successive cancellation decoding scheme is given to construct the multiuser receiver of PC-NOMA. Finally, a low complexity search algorithm is proposed to schedule the NOMA decoding order which improves the error performance by enhanced polarization among user synthesized channels. The block error ratio performances over additive white Gaussian noise channels indicate that the proposed PC-NOMA obviously outperforms the turbo coded NOMA scheme due to the advantages of the two-stage polarization.