Stimulated Raman scattering (SRS) microscopy is a label-free quantitative chemical imaging technique that has demonstrated great utility in biomedical imaging applications ranging from real-time stain-free histopathology to live animal imaging. However, similar to many other nonlinear optical imaging techniques, SRS images often suffer from low signal to noise ratio (SNR) due to absorption and scattering of light in tissue as well as the limitation in applicable power to minimize photodamage. We present the use of a deep learning algorithm to significantly improve the SNR of SRS images. Our algorithm is based on a U-Net convolutional neural network (CNN) and significantly outperforms existing denoising algorithms. More importantly, we demonstrate that the trained denoising algorithm is applicable to images acquired at different zoom, imaging power, imaging depth, and imaging geometries that are not included in the training. Our results identify deep learning as a powerful denoising tool for biomedical imaging at large, with potential towards in vivo applications, where imaging parameters are often variable and ground-truth images are not available to create a fully supervised learning training set.