The use of video segmentation as an early processing step in video analysis lags behind the use of image segmentation for image analysis, despite many available video segmentation methods. A major reason for this lag is simply that videos are an order of magnitude bigger than images; yet most methods require all voxels in the video to be loaded into memory, which is clearly prohibitive for even medium length videos. We address this limitation by proposing an approximation framework for streaming hierarchical video segmentation motivated by data stream algorithms: each video frame is processed only once and does not change the segmentation of previous frames. We implement the graph-based hierarchical segmentation method within our streaming framework; our method is the first streaming hierarchical video segmentation method proposed. We perform thorough experimental analysis on a benchmark video data set and longer videos. Our results indicate the graph-based streaming hierarchical method outperforms other streaming video segmentation methods and performs nearly as well as the full-video hierarchical graph-based method.