In dinoflagellates, the most unique and divergent nuclear organization among the known diversity of eukaryotes has evolved. The list of highly unusual features of dinoflagellate nuclei and genomes is long -- permanently condensed liquid crystalline chromosomes, in which histones are not the main packaging component, genes organized as very long unidirectional gene arrays, general absence of transcriptional regulation, high abundance of the otherwise very rare DNA modification 5-hydroxymethyluracil (5-hmU), and many others. Most of these fascinating properties were originally identified in the 1970s and 1980s but have received very little attention in recent decades using modern genomic tools. In this work, we address some of the outstanding questions regarding dinoflagellate genome organization by mapping the genome-wide distribution of 5-hmU (using both immunoprecipitation-based and basepair-resolution chemical mapping approaches) and of chromatin accessibility in the genome of the dinoflagellate Breviolum minutum. We find that the 5-hmU modification is preferentially enriched over certain classes of repetitive elements, and also often coincides with the boundaries between gene arrays. It is generally anti-correlated with chromatin accessibility, the levels of which are lower in those regions. We discuss the potential roles of 5-hmU in the functional organization of dinoflagellate genomes and its relationship to the transcriptional landscape of gene arrays. Overall design: ATAC-seq in B. minutum mapping of 5-hmU in B. minutum using MeDIP-seq and chemical mapping SMF and ATAC-seq on yeast cells exogenously expressing various dinoflagellate DVNP proteins