There are considerable differences in language processing skill among the normal population. A key question for cognitive science is whether these differences can be ascribed to variations in domain-general cognitive abilities, hypothesized to play a role in language, such as working memory and statistical learning. In this paper, we present experimental evidence pointing to a fundamental memory skill—chunking—as an important predictor of cross-individual variation in complex language processing. Specifically, we demonstrate that chunking ability reflects experience with language, as measured by a serial recall task involving consonant combinations from naturally occurring text. Our results reveal considerable individual differences in participants’ ability to use chunk frequency information to facilitate sequence recall. Strikingly, these differences predict variations across participants in the on-line processing of complex sentences involving relative clauses. Our study thus presents the first evidence tying the fundamental ability for chunking to sentence processing skill, providing empirical support for construction-based approaches.