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A fundamental challenge of shared autonomy is to use high-DoF robots to assist, rather than hinder, humans by first inferring user intent and then empowering the user to achieve their intent. Although successful, prior methods either rely heavily on a priori knowledge of all possible human intents or require many demonstrations and interactions with the human to learn these intents before being able to assist the user. We propose and study a zero-shot, vision-only shared autonomy (VOSA) framework designed to allow robots to use end-effector vision to estimate zero-shot human intents in conjunction with blended control to help humans accomplish manipulation tasks with unknown and dynamically changing object locations. To demonstrate the effectiveness of our VOSA framework, we instantiate a simple version of VOSA on a Kinova Gen3 manipulator and evaluate our system by conducting a user study on three tabletop manipulation tasks. The performance of VOSA matches that of an oracle baseline model that receives privileged knowledge of possible human intents while also requiring significantly less effort than unassisted teleoperation. In more realistic settings, where the set of possible human intents is fully or partially unknown, we demonstrate that VOSA requires less human effort and time than baseline approaches while being preferred by a majority of the participants. Our results demonstrate the efficacy and efficiency of using off-the-shelf vision algorithms to enable flexible and beneficial shared control of a robot manipulator. Code and videos available here: https://sites.google.com/view/zeroshot-sharedautonomy/home