Topologically associating domains (TADs) are fundamental elements of the 3D structure of the eukaryotic genome. However, while the structural importance of the insulator protein CTCF together with cohesin at TAD borders in mammalian cells is well established, the absence of such co-localization at most TAD borders in recent Hi-C studies of D. melanogaster is enigmatic, raising the possibility that these TAD border elements are not generally conserved among metazoans. Using in situ Hi-C with sub-kb resolution, we show that the genome of D. melanogaster is almost completely partitioned into more than 4,000 TADs (median size, 13 kb), nearly 7-fold more than previously identified. The overwhelming majority of these TADs are demarcated by pairs of Drosophila specific insulator proteins, BEAF-32/CP190 or BEAF-32/Chromator, indicating that these proteins may play an analogous role in Drosophila as that of the CTCF/cohesin pair in mammals. Moreover, we find that previously identified TADs enriched for inactive chromatin are predominantly assembled from the higher-level interactions between smaller TADs. In contrast, the contiguous small TADs in regions previously thought to be unstructured "inter-TADs" are organized in an open configuration with far fewer TAD-TAD interactions. Such structures can also be identified in some "inter-TAD" regions of the mammalian genome, suggesting that larger assemblages of small self-associating TADs separated by a "burst" of contiguous small, weakly associating TADs may be a conserved, basic characteristic of the higher order folding of the metazoan genome.