This thesis aims to advance the idea that prosody is fundamentally about creating cohesion, that is, signaling the "relations of meaning that exist within the text" (Halliday & Hasan 1976:4). Building on research on the cohesive function of prosody by Wichmann (2000) and Wennerstrom (2001), I show how each of the features generally referred to as prosodic are used by speakers to lend cohesion to their discourse by signaling the transitions from one unit of discourse to the next, the relations that hold between those units, and their relative prominence. To accomplish this, I look at six prosodic cues in Ekegusii, a Great Lakes Bantu language of southwestern Kenya with lexical and grammatical tone (Cammenga 2002; Nash 2011). Those cues are pause, vowel elision, prosodic accent, pitch reset, isotony (intonational parallelism), and intonational contour. For each feature, I exemplify the ways in which it demarcates conceptually cohesive units of discourse, and/or signals the relations between one unit of speech and another. I show that when these prosodic cues appear, they create cohesive ties between one segment of discourse and another by signaling where one discourse topic ends and another begins, and indicating how -- and how closely -- the new discourse topic relates to the old (Couper-Kuhlen 2004; Swerts & Geluykens 1994). Together with morphosyntactic devices for cohesion, such as anaphoric pronouns and reference, the cohesive ties created by prosody are what give coherence to the text, thus distinguishing it from a random assortment of unrelated utterances (Halliday & Hasan 1976). I conclude by discussing how an understanding of prosody as a means for signaling discourse cohesion complements more interactional approaches to prosody (Barth-Weingarten 2013; Barth-Weingarten & Reber 2010; Couper-Kuhlen & Ford 2004), and provides a language-independent means of examining prosody crosslinguistically, thus laying a foundation for future typological studies.