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We introduce DialectLLM, the first large-scale framework for generating high-quality multi-dialectal conversational data encompassing the three pillars of written dialect -- lexical (vocabulary), orthographic (spelling), and morphosyntactic (grammar) features. DialectLLM produces a dialect-parallel dialog dataset spanning nine English dialects. Partnering with native linguists, we design and validate SAE-to-dialect transformation rules, ensuring authenticity. Our approach challenges the prevailing practice of applying a single morphosyntactic feature set to both user utterances and model responses, showing that models should not reproduce up to 90% of the grammatical features of a dialect. 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