This paper deals with the phonology of word stress in Abkhaz. Stress is both contrastive, forming minimal pairs, and dynamic, with stress placement alternating within morphological paradigms. I evaluate several theories of how Abkhaz stress should be represented, focusing on the size of units which host stress contrasts in the lexicon. A full analysis of Abkhaz stress requires an understanding of schwa, and I present arguments from exceptionless phonotactic restrictions that schwa is predictably epenthesized based on stress. I compile and analyze a corpus of 644 stress alternations, the largest dataset used in the literature. A subset of 426 alternations is used to evaluate four theories, where underlying stress specifications appear once per morpheme (Dybo 1977), syllable (Trigo 1992), mora (Kathman 1992, Vaux and Samuels 2018), or segment (Andersson 2020). The moraic and segmental analyses are the most successful, with 97% and 100% empirical coverage respectively. Arguments from consonant clusters and schwa distribution introduce additional problems for the moraic account, suggesting that Abkhaz stress is a property of individual segments in the lexicon. I conclude that the units capable of bearing stress can be as small as the segment, and may be more crosslinguistically variable than previously assumed.