This paper provides the first discourse parsing experiments with a large language model (LLM) finetuned on corpora annotated in the style of SDRT (Segmented Discourse Representation Theory Asher, 1993; Asher and Lascarides, 2003). The result is a discourse parser, Llamipa (Llama Incremental Parser), that leverages discourse context, leading to substantial performance gains over approaches that use encoder-only models to provide local, context-sensitive representations of discourse units. Furthermore, it can process discourse data incrementally, which is essential for the eventual use of discourse information in downstream tasks.