Modern autonomous vehicles rely heavily on mechanical LiDARs for perception. Current perception methods generally require 360° point clouds, collected sequentially as the LiDAR scans the azimuth and acquires consecutive wedge-shaped slices. The acquisition latency of a full scan (~ 100ms) may lead to outdated perception which is detrimental to safe operation. Recent streaming perception works proposed directly processing LiDAR slices and compensating for the narrow field of view (FOV) of a slice by reusing features from preceding slices. These works, however, are all based on a single modality and require past information which may be outdated. Meanwhile, images from high-frequency cameras can support streaming models as they provide a larger FoV compared to a LiDAR slice. However, this difference in FoV complicates sensor fusion. To address this research gap, we propose an innovative camera-LiDAR streaming 3D object detection framework that uses camera images instead of past LiDAR slices to provide an up-to-date, dense, and wide context for streaming perception. The proposed method outperforms prior streaming models on the challenging NuScenes benchmark. It also outperforms powerful full-scan detectors while being much faster. Our method is shown to be robust to missing camera images, narrow LiDAR slices, and small camera-LiDAR miscalibration.