While most conversational AI systems focus on textual dialogue only, conditioning utterances on visual context (when it's available) can lead to more realistic conversations. Unfortunately, a major challenge for incorporating visual context into conversational dialogue is the lack of large-scale labeled datasets. We provide a solution in the form of a new visually conditioned Future Utterance Prediction task. Our task involves predicting the next utterance in a video, using both visual frames and transcribed speech as context. By exploiting the large number of instructional videos online, we train a model to solve this task at scale, without the need for manual annotations. Leveraging recent advances in multimodal learning, our model consists of a novel co-attentional multimodal video transformer, and when trained on both textual and visual context, outperforms baselines that use textual inputs alone. Further, we demonstrate that our model trained for this task on unlabelled videos achieves state-of-the-art performance on a number of downstream VideoQA benchmarks such as MSRVTT-QA, MSVD-QA, ActivityNet-QA and How2QA.