Morphological Segmentation is a major task in Indigenous language documentation. In this paper we (a) introduce a novel statistical algorithm called Morphemo to split words into their constituent morphemes. We also (b) study how large language models perform on this task. We use these tools to analyze Bribri, an under-resourced Indigenous language from Costa Rica. Morphemo has better performance than the LLM when splitting multimorphemic words, mainly because the LLMs are more conservative, which also gives them an advantage when splitting monomorphemic words. In future work we will use these tools to tag Bribri language corpora, which currently lack morphological segmentation.