Hemichordates, the phylum of bilateral animals closest to chordates, can illuminate the evolutionary origins of various chordate traits to determine whether these were already present in a shared ancestor (the deuterostome ancestor) or were evolved within the chordate line. We find that an anteroposterior map of gene expression domains, representing 42 genes of neural patterning, is closely similar in hemichordates and chordates, though it is restricted to the neural ectoderm in chordates whereas in hemichordates, which have a diffuse nervous system, it encircles the whole body. This map allows an accurate alignment of the anterioposterior axes of members of the two groups. We propose that this map dates back at least to the deuterostome ancestor. The map of dorsoventral expression domains, organized along a Bmp-Chordin developmental axis, is also similar in the two groups in terms of many gene expression domains and for the placement of the gill slits, heart, and post-anal tail. The two groups, however, differ in two major respects along this axis. The nervous system and epidermis are not segregated into distinct territories in hemichordates, as they are in chordates, and furthermore, the mouth is on the Chordin side in hemichordates but the Bmp side in chordates. The dorsoventral dimension has undergone extensive modification in the chordate line, including centralization of the nervous system, segregation of epidermis, derivation of the notochord, perhaps from the gut midline, and relocation of the mouth. Based on the shared domain maps, speculations can be made for the remodeling of the body axis in the chordate line.