Samoan is an ergative-marking, (reportedly) non-tonal Polynesian language in which ergative case is marked segmentally, but absolutive case has been said to be unmarked. This paper shows that in fact, a high edge tone co-occurs with absolutive arguments, based on converging evidence from the phonetic and phonological analysis of intonational patterns in the spoken utterances of a systematically varied set of syntactic structures. This empirical observation raises puzzles that probe the nature of the syntax-prosody interface and the relation between tone and intonation: what is the relation between this absolutive high edge tone and: (i) other case markers in Samoan, which are all segmental?, and (ii) other high edge tones in Samoan that co-occur with fronted expressions and coordination? I propose that: (i) the absolutive high edge tone is a tonal case marker that may be related to an apparently moribund stressed, segmental absolutive particle [ˈia], (ii) the high tones that co-occur with absolutives, fronting, and coordination are all syntactically determined and each inserted in the spellout of distinct syntactic configurations, and (iii) there is another class of edge tones which reliably co-occur with pauses—intonational phrase boundary tones—that are not inserted in spellout but by the phonological grammar. While my proposal may seem surprising at first, I show that it fits the current data better than any alternative.