There is difficulty representing relative clauses with split antecedents (Perlmutter & Ross 1970, McCawley 1982, Link 1984, Wilder 1994, a.o.): (i) Mary met a man and John met a woman who know each other well. In this paper, I demonstrate that existing analyses, both movement and base generation approaches, have difficulties accounting for split-antecedent relative clauses (SARC) without construction-specific stipulations. Even the most promising accounts do not make predictions about the actual behavior of SARC. Formally, I propose that traditional approaches have difficulty because of how the notion of chain is represented. I provide a preliminary analysis using a novel system of representing narrow syntax that does not run into the type of problem that traditional approaches do. SARC are naturally predicted from the way I propose to treat coordination within the new system. In doing this, I argue for another direction of our model of narrow syntax (cf. Vergnaud to appear), one which redefines the representation of a chain and instead represents grammatical relationships as local – a generalized form of Multidominance. This approach to syntax makes wide-reaching predictions, which I do not discuss here. But, I show that this direction derives SARC naturally, without construction-specific stipulations.