We propose a locally hierarchical auto-regressive model with multiple resolutions of discrete codes. In the first stage of our algorithm, we represent an image with a pyramid of codes using Hierarchically Quantized Variational AutoEncoder (HQ-VAE), which disentangles the information contained in the multi-level codes. For an example of two-level codes, we create two separate pathways to carry high-level coarse structures of input images using top codes while compensating for missing fine details by constructing a residual connection for bottom codes. An appropriate selection of resizing operations for code embedding maps enables top codes to capture maximal information within images and the first stage algorithm achieves better performance on both vector quantization and image generation. The second stage adopts Hierarchically Quantized Transformer (HQ-Transformer) to process a sequence of local pyramids, which consist of a single top code and its corresponding bottom codes. Contrary to other hierarchical models, we sample bottom codes in parallel by exploiting the conditional independence assumption on the bottom codes. This assumption is naturally harvested from our first-stage model, HQ-VAE, where the bottom code learns to describe local details. On class-conditional and text-conditional generation benchmarks, our model shows competitive performance to previous AR models in terms of fidelity of generated images while enjoying lighter computational budgets.