We develop a semantic parser that is trained in a grounded setting using pairs of videos captioned with sentences. This setting is both data-efficient, requiring little annotation, and similar to the experience of children where they observe their environment and listen to speakers. The semantic parser recovers the meaning of English sentences despite not having access to any annotated sentences. It does so despite the ambiguity inherent in vision where a sentence may refer to any combination of objects, object properties, relations or actions taken by any agent in a video. For this task, we collected a new dataset for grounded language acquisition. Learning a grounded semantic parser — turning sentences into logical forms using captioned videos — can significantly expand the range of data that parsers can be trained on, lower the effort of training a semantic parser, and ultimately lead to a better understanding of child language acquisition.