Video description is one of the most challenging problems in vision and language understanding due to the large variability both on the video and language side. Models, hence, typically shortcut the difficulty in recognition and generate plausible sentences that are based on priors but are not necessarily grounded in the video. In this work, we explicitly link the sentence to the evidence in the video by annotating each noun phrase in a sentence with the corresponding bounding box in one of the frames of a video. Our dataset, ActivityNet-Entities, augments the challenging ActivityNet Captions dataset with 158k bounding box annotations, each grounding a noun phrase. This allows training video description models with this data, and importantly, evaluate how grounded or "true" such model are to the video they describe. To generate grounded captions, we propose a novel video description model which is able to exploit these bounding box annotations. We demonstrate the effectiveness of our model on our dataset, but also show how it can be applied to image description on the Flickr30k Entities dataset. We achieve state-of-the-art performance on video description, video paragraph description, and image description and demonstrate our generated sentences are better grounded in the video.