In dinoflagellates, a unique and extremely divergent genomic and nuclear organization has evolved. The highly unusual features of dinoflagellate nuclei and genomes include permanently condensed liquid crystalline chromosomes, primarily packaged by proteins other than histones, genes organized in very long unidirectional gene arrays, a general absence of transcriptional regulation, high abundance of the otherwise very rare DNA modification 5-hydroxymethyluracil (5-hmU), and many others. While most of these fascinating properties were originally identified in the 1970s and 1980s, they have not yet been investigated 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 Symbiodiniaceae dinoflagellate Breviolum minutum. We find that the 5-hmU modification is preferentially enriched over certain classes of repetitive elements, often coincides with the boundaries between gene arrays, and is generally correlated with decreased chromatin accessibility, the latter otherwise being largely uniform along the genome. 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.