Dinoflagellate chromosomes represent a unique evolutionary experiment, as they exist in a permanently condensed, liquid crystalline state; are not packaged by histones; and contain genes organized into tandem gene arrays, with minimal transcriptional regulation. We analyze the three-dimensional genome of Breviolum minutum, and find large topological domains (dinoflagellate topologically associating domains, which we term 'dinoTADs') without chromatin loops, which are demarcated by convergent gene array boundaries. Transcriptional inhibition disrupts dinoTADs, implicating transcription-induced supercoiling as the primary topological force in dinoflagellates.