It is now well established that eukaryote genomes have a common architectural organization into topologically associated domains (TADs) and evidence is accumulating that this organization plays an important role in gene regulation. However, the mechanisms that partition the genome into TADs and the nature of domain boundaries are still poorly understood. We have investigated boundary regions in the Drosophila genome and find that they can be identified as domains of very low H3K27me3. The genome-wide H3K27me3 profile partitions into two states; very low H3K27me3 identifies Depleted (D) domains that contain housekeeping genes and their regulators such as the histone acetyltransferase-containing NSL complex, whereas domains containing moderate-to-high levels of H3K27me3 (Enriched or E domains) are associated with regulated genes, irrespective of whether they are active or inactive. The D domains correlate with the boundaries of TADs and are enriched in a subset of architectural proteins, particularly Chromator, BEAF-32, and Z4/Putzig. However, rather than being clustered at the borders of these domains, these proteins bind throughout the H3K27me3-depleted regions and are much more strongly associated with the transcription start sites of housekeeping genes than with the H3K27me3 domain boundaries. While we have not demonstrated causality, we suggest that the D domain chromatin state, characterised by very low or absent H3K27me3 and established by housekeeping gene regulators, acts to separate topological domains thereby setting up the domain architecture of the genome.