Most known giant viruses, i.e., viruses producing giant virions, parasitize amoebae and other unicellular eukaryotes. Although they vary in the level of dependence on host nuclear functions, their virions self-assemble in the host cell's cytoplasm. Here we report the discovery of a new prototype of giant virus infecting epidermal cells of the marine arrow worm Adhesisagitta hispida. Its 1.25 μm-long virions self-assemble and accumulate in the host cell's nucleus. Conventional transmission electron microscopy reveals that the virions have a unique bipartite structure. An ovoid nucleocapsid, situated in a broad "head" end of the virion is surrounded by a thin envelope. The latter extends away from the head to form a voluminous conical "tail" filled with electron-dense extracapsidular material. The 31nm-thick capsid wall has a distinctive substructure resulting from a patterned arrangement of subunits; it bears no ultrastructural resemblance to the virion walls of other known giant viruses. The envelope self-assembles coincident with the capsid and remotely from all host membranes. We postulate that transmission to new hosts occurs by rupture of protruding virion-filled nuclei when infected arrow worms mate. Future genomic work is needed to determine the phylogenetic position of this new virus, which we have provisionally named Meelsvirus.