Demonstrating the veracity of videos is a longstanding problem that has recently become more urgent and acute. It is extremely hard to accurately detect manipulated videos using content analysis, especially in the face of subtle, yet effective, manipulations, such as frame rate changes or skin tone adjustments. One prominent alternative to content analysis is to securely embed provenance information into videos. However, prior approaches have poor performance and/or granularity that is too coarse. To this end, we construct Vronicle -- a video provenance system that offers fine-grained provenance information and substantially better performance. It allows a video consumer to authenticate the camera that originated the video and the exact sequence of video filters that were subsequently applied to it. Vronicle exploits the increasing popularity and availability of Trusted Execution Environments (TEEs) on many types of computing platforms. One contribution of Vronicle is the design of provenance information that allows the consumer to verify various aspects of the video, thereby defeating numerous fake-video creation methods. Vronicle's adversarial model allows for a powerful adversary that can manipulate the video (e.g., in transit) and the software state outside the TEE. Another contribution is the use of fixed-function Intel SGX enclaves to post-process videos. This design facilitates verification of provenance information. We present a prototype implementation of Vronicle (to be open sourced), which relies on current technologies, making it readily deployable. Our evaluation demonstrates that Vronicle's performance is well-suited for offline use-cases.