Chromatin accessibility plays an important role in shaping gene expression patterns across development and evolution; however, little is known about the genetic and molecular mechanisms that influence chromatin configuration itself. Because cis and trans influences can both theoretically influence the accessibility of the epigenome, we sought to better characterize the role that both of these mechanisms play in altering chromatin accessibility in two closely related sea urchin species. Using hybrids of the two species, and adapting a statistical framework previously developed for the analysis of cis and trans influences on the transcriptome, we examined how these mechanisms shape the regulatory landscape at three important developmental stages, and compared our results to similar patterns in the transcriptome. We found extensive cis- and trans-based influences on evolutionary changes in chromatin, with cis effects slightly more numerous and larger in effect. Genetic mechanisms influencing gene expression and chromatin configuration are correlated, but differ in several important ways. Maternal influences also appear to have more of an effect on chromatin accessibility than on gene expression, persisting well past the maternal-to-zygotic transition. Furthermore, chromatin accessibility near GRN genes appears to be regulated differently than the rest of the epigenome, and indicates that trans factors may play an outsized role in the configuration of chromatin near these genes. Together, our results represent the first attempt to quantify cis and trans influences on evolutionary divergence in chromatin configuration in an outbred natural study system, and suggest that the regulation of chromatin is more genetically complex than was previously appreciated.