Self-supervised learning holds the promise of learning good representations from real-world continuous uncurated data streams. However, most existing works in visual self-supervised learning focus on static images or artificial data streams. Towards exploring a more realistic learning substrate, we investigate streaming self-supervised learning from long-form real-world egocentric video streams. Inspired by the event segmentation mechanism in human perception and memory, we propose "Memory Storyboard," a novel continual self-supervised learning framework that groups recent past frames into temporal segments for a more effective summarization of the past visual streams for memory replay. To accommodate efficient temporal segmentation, we propose a two-tier memory hierarchy: the recent past is stored in a short-term memory, where the storyboard temporal segments are produced and then transferred to a long-term memory. Experiments on two real-world egocentric video datasets show that contrastive learning objectives on top of storyboard frames result in semantically meaningful representations that outperform those produced by state-of-the-art unsupervised continual learning methods.