A light field is a collection of multiview images which represent a three-dimensional scene. Rendering from a light field provides a simple and efficient way to generate arbitrary new views of the scene, bypassing the difficult problem of acquiring accurate geometric and photometric models. The enormous amount of data required in a light field poses a key challenge in rendering. Tree-structured vector quantization (TSVQ) provides a moderate compression ratio of around 24:1, which alleviates, but does not solve, the problem. Compression schemes based on video coding techniques exploit the data redundancy very effectively, but do not provide adequate random access for rendering. The paper presents an analysis of the data-access pattern during the rendering process and describes a compression scheme that supports interactive rendering directly from compressed light field data. The proposed algorithm provides a high compression ratio of as much as ten times that of TSVQ, while slowing down the rendering speed by only a factor smaller than 2.