We develop streaming keyword spotting systems using a recurrent neural network transducer (RNN-T) model: an all-neural, end-to-end trained, sequence-to-sequence model which jointly learns acoustic and language model components. Our models are trained to predict either phonemes or graphemes as subword units, thus allowing us to detect arbitrary keyword phrases, without any out-of-vocabulary words. In order to adapt the models to the requirements of keyword spotting, we propose a novel technique which biases the RNN-T system towards a specific keyword of interest. Our systems are compared against a strong sequence-trained, connectionist temporal classification (CTC) based “keyword-filler” baseline, which is augmented with a separate phoneme language model. Overall, our RNN-T system with the proposed biasing technique significantly improves performance over the baseline system.