Every biology student gets introduced to the chordates with a list of their distinctive characteristics: they have a notochord, a dorsal hollow nerve cord, gill slits, and a post-anal tail. The embryonic stage in which we express all of these features is called the pharyngula stage—it's often also the only stage at which we have them. We terrestrial vertebrates seal off those pharyngeal openings as we develop, while sea squirts throw away their brains as an adult.
The chordate phylum has all four of those traits, but there is another extremely interesting phylum that has some of them, the hemichordates. The hemichordates are marine worms that have gill slits and a stub of a tail. They also have a bundle of nerves in the right place to be a dorsal nerve cord, but the latest analyses suggest that it's not discrete enough to count—they have more of a diffuse nerve net than an actual central nervous system. They don't really have a notochord, but they do have a stiff array of cells in their proboscis that vaguely resembles one. They really are "half a chordate" in that they only partially express characters that are defining elements of the chordate body plan. Of course, they also have a unique body plan of their own, and are quite lovely animals in their own right. They are a sister phylum to the chordates, and the similarities and differences between us tell us something about our last common ancestor, the ur-deuterostome.
Analyzing morphology is one approach, but this is the age of molecular biology, so digging deeper and comparing genes gives us a sharper picture of relationships. This is also the early days of evo-devo, and an even more revealing way to examine related phyla is to look at patterns of gene regulation—how those genes are turned on and off in space and time during the development of the organism—and see how those relate. Gerhart, Lowe, and Kirschner have done just that in hemichordates, and have results that strengthen the affinities between chordates and hemichordates. (By the way, Gerhart and Kirschner also have a new book out, The Plausibility of Life (amzn/b&n/abe/pwll), which I'll review as soon as I get the time to finish it.)