Chatbots built upon language models have exploded in popularity, but they have largely been limited to synchronous, turn-by-turn dialogues. In this paper we present a simple yet general method to simulate real-time interactive conversations using pretrained text-only language models, by modeling timed diarized transcripts and decoding them with causal rejection sampling. We demonstrate the promise of this method with two case studies: instant messenger dialogues and spoken conversations, which require generation at about 30 tok/s and 20 tok/s respectively to maintain real-time interactivity. These capabilities can be added into language models using relatively little data and run on commodity hardware.