It is customary nowadays that large web objects are cached somewhere close to the user. This saves traffic upstream of the cache and offers the users a better responsiveness. Caching algorithms typically rank the objects in some way and cache the top-ranked objects. In this paper we study a scenario in which a requested video is (instantaneously) streamed to the user and in which the video library is highly dynamic: new videos are frequently introduced, get popular, get consumed and fade away. Caching streaming videos differs from caching traditional web objects as the former are consumed as their information trickles in, while the latter have to be downloaded (almost) completely before they can be consumed. We develop a caching algorithm specifically for streaming video taking into account the dynamicity of the library. First we make sure that its ranking algorithm can follow the dynamicity of the library (better than traditional algorithms can). Second we segment each video in chunks and propose a new algorithm to rank these chunks. We compare the performance of caching based on this new ranking algorithm with traditional caching algorithms and show that chunking is most beneficial.