Multimodal search-based dialogue is a challenging new task: It extends visually grounded question answering systems into multi-turn conversations with access to an external database. We address this new challenge by learning a neural response generation system from the recently released Multimodal Dialogue (MMD) dataset (Saha et al., 2017). We introduce a knowledge-grounded multimodal conversational model where an encoded knowledge base (KB) representation is appended to the decoder input. Our model substantially outperforms strong baselines in terms of text-based similarity measures (over 9 BLEU points, 3 of which are solely due to the use of additional information from the KB.