We introduce the Globally Normalized Autoregressive Transducer (GNAT) for addressing the label bias problem in streaming speech recognition. Our solution admits a tractable exact computation of the denominator for the sequence-level normalization. Through theoretical and empirical results, we demonstrate that by switching to a globally normalized model, the word error rate gap between streaming and non-streaming speech-recognition models can be greatly reduced (by more than 50% on the Librispeech dataset). This model is developed in a modular framework which encompasses all the common neural speech recognition models. The modularity of this framework enables controlled comparison of modelling choices and creation of new models. A JAX implementation of our models has been open sourced.