We present TabPFN, a trained Transformer that can do supervised classification for small tabular datasets in less than a second, needs no hyperparameter tuning and is competitive with state-of-the-art classification methods. TabPFN is fully entailed in the weights of our network, which accepts training and test samples as a set-valued input and yields predictions for the entire test set in a single forward pass. TabPFN is a Prior-Data Fitted Network (PFN) and is trained offline once, to approximate Bayesian inference on synthetic datasets drawn from our prior. This prior incorporates ideas from causal reasoning: It entails a large space of structural causal models with a preference for simple structures. On 30 datasets from the OpenML-CC18 suite, we show that our method clearly outperforms boosted trees and performs on par with complex state-of-the-art AutoML systems with up to 70× speedup. This increases to a 3 200× speedup when a GPU is available. We provide all our code, the trained TabPFN, an interactive browser demo and a Colab notebook at https://github.com/tabpfn-anonym/TabPFNAnonym.