Is language distinct from other cognition? Does the neural machinery for language emerge from general-purpose neural mechanisms early in development, becoming tuned for language only after years of experience and maturation? In adults, language is supported by a frontotemporal network that is functionally and connectionally dissociated from adjacent domain-general cortex supporting other, more general cognitive functions. We scanned young children (2-9 years of age) on an auditory language localizer, spatial working memory localizer (engaging the domain-general multiple demand (MD) network), and a resting state scan. Subject-specific functional regions of interest (fROIs) defined with the language task showed consistent selectivity to auditory sentences in key left hemisphere regions, and were not engaged for spatial working memory, showing similar domain-specificity as reported in adults; and despite known prolonged development of frontal cortices, the left inferior frontal cortex (“Broca’s area”) showed some of the most robust specificity for linguistic content. Thus, despite immature language skills, young children already have left-lateralized brain regions dedicated to linguistic content. Children also showed higher within-network (language-language) connectivity than between-network connectivity (language-to-MD fROIs defined with the working memory task), in both hemispheres, but with higher within-network connectivity on the left. Language-selectivity increased with age (replicated in a subset of children scanned longitudinally) while specificity of language connectivity did not change with age (again replicated longitudinally), suggesting that connectivity is more static than, and may perhaps earmark, functional specificity. By age 2, the language network is specialized for linguistic processing (domain-specific) function, is distinct from adjacent cortex, and is not engaged in other higher-order cognitive processing.