We introduce a pioneering autoregressive generative model for 3D point cloud generation. Inspired by visual autoregressive modeling (VAR), we conceptualize point cloud generation as an autoregressive up-sampling process. This leads to our novel model, PointARU, which progressively refines 3D point clouds from coarse to fine scales. PointARU follows a two-stage training paradigm: first, it learns multi-scale discrete representations of point clouds, and then it trains an autoregressive transformer for next-scale prediction. To address the inherent unordered and irregular structure of point clouds, we incorporate specialized point-based up-sampling network modules in both stages and integrate 3D absolute positional encoding based on the decoded point cloud at each scale during the second stage. Our model surpasses state-of-the-art (SoTA) diffusion-based approaches in both generation quality and parameter efficiency across diverse experimental settings, marking a new milestone for autoregressive methods in 3D point cloud generation. Furthermore, PointARU demonstrates exceptional performance in completing partial 3D shapes and up-sampling sparse point clouds, outperforming existing generative models in these tasks.