This article examines a puzzle pertaining to the distribution of covalued nominals in two understudied Mayan languages, Chuj and Ch’ol. While Ch’ol behaves as expected with regard to the binding conditions, Chuj appears to consistently tolerate violations of Condition C. The Chuj data thus cast doubt on the widely held view that the binding conditions reflect a universal property of human language (e.g., Grodzinsky and Reinhart 1993, Reuland 2011). I argue that the difference between Chuj and Ch’ol can be largely explained if, contrary to Ch’ol, Chuj exhibits “high-absolutive” syntax, independently proposed by Coon, Mateo Pedro, and Preminger (2014) to explain a constellation of morphosyntactic properties shared by a subset of Mayan languages. This syntax bleeds otherwise expected binding relations from the subject into the object, explaining the apparent violations. I further show that linear precedence plays a fundamental role in regulating the distribution of covalued nominals across Mayan, which I argue is due to a general ban on cataphoric “free” pronouns. Thus, the Mayan data not only are consistent with the binding conditions, but also provide further evidence in favor of a deep typological parameter within the Mayan language family.