Using dynamic systems theory tools (Verspoor et al. 2011) within the framework of fluency, complexity, and accuracy (Skehan 1998; Norris and Ortega 2009), this study asserts that an untutored (Turkish) immigrant English language learner may over one year cultivate advanced lexical and syntactic abilities, but attaining grammatical precision without instruction might prove tougher. In general, dynamic systems theory appears an apt framework for exploring the linguistic growth of advanced naturalistic untutored immigrant and refugee learners.