The relationship between chromatin organization and gene regulation remains unclear. While disruption of chromatin domains and domain boundaries can lead to misexpression of developmental genes, acute depletion of regulators of genome organization has a relatively small effect on gene expression. It is therefore uncertain whether gene expression and chromatin state drive chromatin organization or whether changes in chromatin organization facilitate cell-type-specific activation of gene expression. Here, using the dorsoventral patterning of the Drosophila melanogaster embryo as a model system, we provide evidence for the independence of chromatin organization and dorsoventral gene expression. We define tissue-specific enhancers and link them to expression patterns using single-cell RNA-seq. Surprisingly, despite tissue-specific chromatin states and gene expression, chromatin organization is largely maintained across tissues. Our results indicate that tissue-specific chromatin conformation is not necessary for tissue-specific gene expression but rather acts as a scaffold facilitating gene expression when enhancers become active.