Aptitude for and proficiency in acquiring new languages varies in the human population but their neural bases are largely unknown. We investigated the influence of cortical thickness on language learning predictors measured by the LLAMA tests and a pitch-change discrimination test. The LLAMA tests are first language-independent assessments of language learning aptitude for vocabulary, phonetic working memory, sound-symbol correspondence (not used in this study), and grammatical inferencing. Pitch perception proficiency is known to predict aptitude for learning new phonology. Results show a correlation between scores in a grammatical meaning-inferencing aptitude test and cortical thickness of Broca's area (r(30) = 0.65, p = 0.0202) and other frontal areas (r(30) = 0.66, p = 0.0137). Further, a correlation was found between proficiency in discriminating pitch-change direction and cortical thickness of the right Broca homologue (r(30) = 0.57, p = 0.0006). However, no correlations were found for aptitude for vocabulary learning or phonetic working memory. Results contribute to locating cortical regions important for language-learning aptitude.