In this paper we present VDTTS, a Visually-Driven Text-to-Speech model. Motivated by dubbing, VDTTS takes advantage of video frames as an additional input alongside text, and generates speech that matches the video signal. We demonstrate how this allows VDTTS to, unlike plain TTS models, generate speech that not only has prosodic variations like natural pauses and pitch, but is also synchronized to the input video. Experimentally, we show our model produces well synchronized outputs, approaching the video-speech synchronization quality of the ground-truth, on several challenging benchmarks including "in-the-wild" content from VoxCeleb2. We encourage the reader to view the demo videos demonstrating video-speech synchronization, robustness to speaker ID swapping, and prosody.