Cosmic ray (CR) identification and replacement are critical components of imaging and spectroscopic reduction pipelines involving solid-state detectors. We present deepCR, a deep-learning-based framework for CR identification and subsequent image inpainting based on the predicted CR mask. To demonstrate the effectiveness of this framework, we train and evaluate models on Hubble Space Telescope (HST) ACS/WFC images of sparse extragalactic fields, globular clusters, and resolved galaxies. We demonstrate that at a false-positive rate of 0.5%, deepCR achieves close to 100% detection rates in both extragalactic and globular cluster fields, and 91% in resolved galaxy fields, which is a significant improvement over the current state-of-the-art method LACosmic. Compared with a multicore CPU implementation of LACosmic, deepCR CR mask predictions run up to 6.5 times faster on a CPU and 90 times faster on a single GPU. For image inpainting, the mean squared errors of deepCR predictions are 20 times lower in globular cluster fields, 5 times lower in resolved galaxy fields, and 2.5 times lower in extragalactic fields, compared with the best performing nonneural technique tested. We present our framework and the trained models as an open-source Python project , with a simple-to-use API. To facilitate reproducibility of the results we also provide a benchmarking codebase .