Actually, they aren't vertebrates at all. They are, however, the invertebrates most closely related to vertebrates. Tunicates are in the phylum Chordata, which includes the vertebrates and another invertebrate called a lancelet, but tunicates themselves are not vertebrates. They do possess a notochord, which in vertebrates, turns into the vertebral column, but in tunicates and lancelets, the notochord never develops into a vertebral column, hence they are not classified as vertebrates and instead have their own classification in the Subphyla Urochordata and Cephalochordata (vertebrates are in the Subphyla Craniata).