We present GigaPose, a fast, robust, and accurate method for CAD-based novel object pose estimation in RGB images. GigaPose first leverages discriminative templates, rendered images of the CAD models, to recover the out-of-plane rotation and then uses patch correspondences to estimate the four remaining parameters. Our approach samples templates in only a two-degrees-of-freedom space instead of the usual three and matches the input image to the templates using fast nearest-neighbor search in feature space, results in a speedup factor of 38x compared to the state of the art. Moreover, GigaPose is significantly more robust to segmentation errors. Our extensive evaluation on the seven core datasets of the BOP challenge demonstrates that it achieves state-of-the-art accuracy and can be seamlessly integrated with a refinement method. Additionally, we show the potential of GigaPose with 3D models predicted by recent work on 3D reconstruction from a single image, relaxing the need for CAD models and making 6D pose object estimation much more convenient. We will make the code and trained models publicly available.