Eye gaze contains rich information about human attention and cognitive processes. This capability makes the underlying technology, known as gaze tracking, a critical enabler for many ubiquitous applications and has triggered the development of easy-to-use gaze estimation services. Indeed, by utilizing the ubiquitous cameras on tablets and smartphones, users can readily access many gaze estimation services. In using these services, users must provide their full-face images to the gaze estimator, which is often a black box. This poses significant privacy threats to the users, especially when a malicious service provider gathers a large collection of face images to classify sensitive user attributes. In this work, we present PrivateGaze, the first approach that can effectively preserve users' privacy in black-box gaze tracking services without compromising gaze estimation performance. Specifically, we proposed a novel framework to train a privacy preserver that converts full-face images into obfuscated counterparts, which are effective for gaze estimation while containing no privacy information. Evaluation on four datasets shows that the obfuscated image can protect users' private information, such as identity and gender, against unauthorized attribute classification. Meanwhile, when used directly by the black-box gaze estimator as inputs, the obfuscated images lead to comparable tracking performance to the conventional, unprotected full-face images.