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Many modern robotics systems employ LiDAR as their main sensing modality due to its geometrical richness. Rolling shutter LiDARs are particularly common, in which an array of lasers scans the scene from a rotating base. Points are emitted as a stream of packets, each covering a sector of the 360° coverage. Modern perception algorithms wait for the full sweep to be built before processing the data, which introduces an additional latency. For typical 10Hz LiDARs this will be 100ms. As a consequence, by the time an output is produced, it no longer accurately reflects the state of the world. This poses a challenge, as robotics applications require minimal reaction times, such that maneuvers can be quickly planned in the event of a safety-critical situation. In this paper we propose StrObe, a novel approach that minimizes latency by ingesting LiDAR packets and emitting a stream of detections without waiting for the full sweep to be built. StrObe reuses computations from previous packets and iteratively updates a latent spatial representation of the scene, which acts as a memory, as new evidence comes in, resulting in accurate low-latency perception. We demonstrate the effectiveness of our approach on a large scale real-world dataset, showing that StrObe far outperforms the state-of-the-art when latency is taken into account, and matches the performance in the traditional setting.