A low-complexity coding scheme is developed to achieve the rate region of maximum likelihood decoding for interference channels. As in the classical rate-splitting multiple access scheme by Grant, Rimoldi, Urbanke, and Whiting, the proposed coding scheme uses superposition of multiple codewords with successive cancellation decoding, which can be implemented using standard point-to-point encoders and decoders. Unlike rate-splitting multiple access, which is not rate-optimal for multiple receivers, the proposed coding scheme transmits codewords over multiple blocks in a staggered manner and recovers them successively over sliding decoding windows, achieving the single-stream optimal rate region as well as the more general Han--Kobayashi inner bound for the two-user interference channel. The feasibility of this scheme in practice is verified by implementing it using commercial channel codes over the two-user Gaussian interference channel.