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Autonomous vehicles operate in a dynamic environment, where the speed with which a vehicle can perceive and react impacts the safety and efficacy of the system. LiDAR provides a prominent sensory modality that informs many existing perceptual systems including object detection, segmentation, motion estimation, and action recognition. The latency for perceptual systems based on point cloud data can be dominated by the amount of time for a complete rotational scan (e.g. 100 ms). This built-in data capture latency is artificial, and based on treating the point cloud as a camera image in order to leverage camera-inspired architectures. However, unlike camera sensors, most LiDAR point cloud data is natively a streaming data source in which laser reflections are sequentially recorded based on the precession of the laser beam. In this work, we explore how to build an object detector that removes this artificial latency constraint, and instead operates on native streaming data in order to significantly reduce latency. This approach has the added benefit of reducing the peak computational burden on inference hardware by spreading the computation over the acquisition time for a scan. We demonstrate a family of streaming detection systems based on sequential modeling through a series of modifications to the traditional detection meta-architecture. We highlight how this model may achieve competitive if not superior predictive performance with state-of-the-art, traditional non-streaming detection systems while achieving significant latency gains (e.g. 1/15'th - 1/3'rd of peak latency). Our results show that operating on LiDAR data in its native streaming formulation offers several advantages for self driving object detection -- advantages that we hope will be useful for any LiDAR perception system where minimizing latency is critical for safe and efficient operation.