Image and text retrieval is one of the foundational tasks in the vision and language domain with multiple real-world applications. State-of-the-art contrastive approaches, e.g. CLIP, ALIGN, represent images and texts as dense embeddings and calculate the similarity in the dense embedding space as the matching score. On the other hand, sparse semantic features like bag-of-words models are more interpretable, but believed to suffer from inferior accuracy than dense representations. In this work, we show that it is possible to build a sparse semantic representation that is as powerful as, or even better than, dense presentations. We extend the CLIP model and build a sparse text and image representation (STAIR), where the image and text are mapped to a sparse token space. Each token in the space is a (sub-)word in the vocabulary, which is not only interpretable but also easy to integrate with existing information retrieval systems. STAIR model significantly outperforms a CLIP model with +4.9% and +4.3% absolute Recall@1 improvement on COCO-5k text→image and image→text retrieval respectively. It also achieved better performance on both of ImageNet zero-shot and linear probing compared to CLIP.