We introduce Speech ReaLLM, a new ASR architecture that marries "decoder-only" ASR with the RNN-T to make multimodal LLM architectures capable of real-time streaming. This is the first "decoder-only" ASR architecture designed to handle continuous audio without explicit end-pointing. Speech ReaLLM is a special case of the more general ReaLLM ("real-time LLM") approach, also introduced here for the first time. The idea is inspired by RNN-T: Instead of generating a response only at the end of a user prompt, generate after every input token received in real time (it is often empty). On Librispeech "test", an 80M Speech ReaLLM achieves WERs of 3.0% and 7.4% in real time (without an external LM or auxiliary loss). This is only slightly above a 3x larger Attention-Encoder-Decoder baseline. We also show that this way, an LLM architecture can learn to represent and reproduce the flow of time; and that a pre-trained 7B LLM can be fine-tuned to do reasonably well on this task.