How individuals learn complex regularities in the environment and generalize them to new instances is a key question in cognitive science. Although previous investigations have advocated the idea that learning and generalizing depend upon separate processes, the same basic learning mechanisms may account for both. In language learning experiments, these mechanisms have typically been studied in isolation of broader cognitive phenomena such as memory, perception, and attention. Here, we show how learning and generalization in language is embedded in these broader theories by testing learners on their ability to chunk nonadjacent dependencies—a key structure in language but a challenge to theories that posit learning through the memorization of structure. In two studies, adult participants were trained and tested on an artificial language containing nonadjacent syllable dependencies, using a novel chunking-based serial recall task involving verbal repetition of target sequences (formed from learned strings) and scrambled foils. Participants recalled significantly more syllables, bigrams, trigrams, and nonadjacent dependencies from sequences conforming to the language’s statistics (both learned and generalized sequences). They also encoded and generalized specific nonadjacent chunk information. These results suggest that participants chunk remote dependencies and rapidly generalize this information to novel structures. The results thus provide further support for learning-based approaches to language acquisition, and link statistical learning to broader cognitive mechanisms of memory.