In mid-20th century, the linguist Noam Chomsky established generative linguistics, and made significant contributions to linguistics, computer science, and cognitive science by developing the computational and philosophical foundations for a theory that defined language as a formal system, instantiated in human minds or artificial machines. These developments in turn ushered a wave of research on symbolic Artificial Intelligence (AI). More recently, a new wave of non-symbolic AI has emerged with neural Language Models (LMs) that exhibit impressive linguistic performance, leading many to question the older approach and wonder about the the compatibility of generative AI and generative linguistics. In this paper, we argue that generative AI is compatible with generative linguistics and reinforces its basic tenets in at least three ways. First, we argue that LMs are formal generative models as intended originally in Chomsky's work on formal language theory. Second, LMs can help develop a program for discovery procedures as defined by Chomsky's "Syntactic Structures". Third, LMs can be a major asset for Chomsky's minimalist approach to Universal Grammar and language acquisition. In turn, generative linguistics can provide the foundation for evaluating and improving LMs as well as other generative computational models of language.