A new research paradigm is proposed that leverages developer eye gaze to improve the state of the art in software engineering research and practice. The vision of this new paradigm for use on software engineering tasks such as code summarization, code recommendations, prediction, and continuous traceability is described. Based on this new paradigm, it is foreseen that new benchmarks will emerge based on developer gaze. The research borrows from cognitive psychology, artificial intelligence, information retrieval, and data mining. It is hypothesized that new algorithms will be discovered that work with eye gaze data to help improve current IDEs, thus improving developer productivity. Conducting empirical studies using an eye tracker will lead to inventing, evaluating, and applying innovative methods and tools that use eye gaze to support the developer. The implications and challenges of this paradigm for future software engineering research is discussed.