Accurate eye segmentation can improve eye-gaze estimation and support interactive computing based on visual attention; however, existing eye segmentation methods suffer from issues such as person-dependent accuracy, lack of robustness, and an inability to be run in real-time. Here, we present the RITnet model, which is a deep neural network that combines U-Net and DenseNet. RITnet is under 1 MB and achieves 95.3% accuracy on the 2019 OpenEDS Semantic Segmentation challenge. Using a GeForce GTX 1080 Ti, RITnet tracks at $>$> 300Hz, enabling real-time gaze tracking applications. Pre-trained models and source code are available https://bitbucket.org/eye-ush/ritnet/.