This longitudinal case study follows a dynamic systems approach to investigate an under-studied research area in second language acquisition, the development of complexity and accuracy for an advanced untutored learner of English. Using the analytical tools of dynamic systems theory (Verspoor et al. 2011) within the framework of complexity, accuracy, and fluency (Skehan 1998; Norris and Ortega 2009), the study tracks accuracy, syntactic complexity, and lexical diversity in the speech of a Turkish immigrant over one year. Results from these oral interviews show that most development occurred in the participant's lexical diversity, syntactic complexity showed potential but unverifiable gains, and accuracy showed no development. These findings suggest that an untutored language learner may develop advanced lexical and syntactic skills, but achieving grammatical accuracy without instruction may be more difficult. Overall, dynamic systems theory seems to provide a suitable framework for examining the linguistic development of advanced naturalistic learners, with important implications for future research involving untutored immigrant and refugee populations of English language learners.