This article addresses the autonomy hypothesis of vocabulary and grammar and bootstrapping mechanisms in early language development. Two birth cohorts of 1,505 and 1,049 same-sex twin pairs from the UK were assessed at 2 and 3 years on grammar and vocabulary, using adapted versions of the MacArthur Communicative Development Inventory. Vocabulary and grammar correlate strongly at both 2 and 3 years in both cohorts. Multivariate genetic modeling reveals a consistently high genetic correlation between vocabulary and grammar at 2 and 3 years. This finding suggests the same genetic influences operate for both vocabulary and grammar, a finding incompatible with traditional autonomy hypothesis, at least in early acquisition. Crosslagged longitudinal genetic models indicate both lexical and syntactical bootstrapping operate from 2 to 3 years.