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Monaural speech separation is the task of separating target speech from interference in single-channel recordings. Although substantial progress has been made recently in deep learning based speech separation, previous studies usually focus on a single type of interference, either background noise or competing speakers. In this study, we address both speech and nonspeech interference, i.e., monaural speaker separation in noise, in a talker-independent fashion. We extend a recently proposed deep CASA system to deal with noisy speaker mixtures. To facilitate speech enhancement, a denoising module is added to deep CASA as a front-end processor. The proposed systems achieve state-of-the-art results on a benchmark noisy two-speaker separation dataset. The denoising module leads to substantial performance gain across various noise types, and even better generalization in noise-free conditions.