We introduce LegoGPT, the first approach for generating physically stable LEGO brick models from text prompts. To achieve this, we construct a large-scale, physically stable dataset of LEGO designs, along with their associated captions, and train an autoregressive large language model to predict the next brick to add via next-token prediction. To improve the stability of the resulting designs, we employ an efficient validity check and physics-aware rollback during auto-regressive inference, which prunes infeasible token predictions using physics laws and assembly constraints. Our experiments show that LegoGPT produces stable, diverse, and aesthetically pleasing LEGO designs that align closely with the input text prompts. We also develop a text-based LEGO texturing method, enabling us to generate colored and textured designs. We show that our designs can be assembled by humans manually as well as by robotic arms automatically. Upon publication, we will release our new dataset, StableText2Lego, which contains over 47,000 LEGO structures of over 28,000 unique 3D objects accompanied by detailed captions, along with our code and models.