This is my MPhil thesis for my degree in General Linguistics and Comparative Philology at Oxford. It gives an overview of Swahili syntax, along with the linguistic theory of Lexical-Functional Grammar, and uses this theory to propose a new model for analyzing relative clauses in Swahili. Ultimately I argue that the conceptual resources of Lexical-Functional Grammar offer a better explanation of relative syntax than previous work was able to achieve.