A remarkable sponge with unprecedented megascleres and systematic affinities was collected recently from a previously unidentified volcano on Colville Ridge to the north-east of New Zealand. The sponge has the appearance of a tetillid sponge (family Tetillidae Sollas, 1886) with a perfectly spherical external form, radiating internal skeleton of huge oxeas and triaenes, and microspined sigmaspires as microscleres. The triaene megascleres, however, are unprecedented in their form and ornamentation; they are huge clubbed orthotriaenes the upper third of which is acanthose. Stupenda singularis gen. et sp. nov. is described here and the phylogenetic affinity and taxonomic position of this unique sponge is explored in relation to a broad range of tetractinellid sponges (order Tetractinellida Marshall, 1876) using the Folmer?+?Erpenbeck fragment of the cytochrome c oxidase subunit I (COI) gene and a nearly complete sequence of the 18S rDNA gene. Mitochondrial introns are rare in sponges but S.?singularis gen. et sp. nov. possesses a mitochondrial group I intron at position 387 in COI; it hosts a putative LAGLIDADG endonuclease gene. This intron is the first of its kind in sponges: the self-splicing intron is homologous to a placozoan COI intron whereas the LAGLIDADG endonuclease gene may be related to Fungi LAGLIDADG endonuclease genes.