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We develop an end-to-end deep learning-based approach for the classification of complex maritime environments via multichannel synthetic aperture radar (MSAR) sensors. In particular, we introduce a novel convolutional neural network (CNN)-based multichannel structure that incorporates a divisive normalization technique that is critical for achieving consistent classification performance across maritime scenes. We evaluate the performance of our technique, called MSAR-Net, using datasets collected by the U.S. Naval Research Laboratory's experimental airborne MSAR system. Our results demonstrate that MSAR-Net achieves consistently and substantially superior performance compared to conventional amplitude-based scene classification. Finally, though we focus on the specific (yet difficult) problem of maritime surveillance, MSAR-Net, introduced in this article, is a fundamental technique that can potentially result in significant performance improvements in a variety of multichannel surveillance and remote sensing applications.