We report evidence of ordered orbital motion in luminous star-forming galaxies at z∼ 1.3. We present integral field spectroscopy (IFS) observations, performed with the OH Suppressing InfraRed Imaging Spectrograph (OSIRIS) system, assisted by laser guide star adaptive optics on the Keck telescope, of 13 star-forming galaxies selected from the WiggleZ Dark Energy Survey. Selected via ultraviolet and [O ii] emission, the large volume of the WiggleZ survey allows the selection of sources which have comparable intrinsic luminosity and stellar mass to IFS samples at z > 2. Multiple 1–2 kpc size subcomponents of emission, or ‘clumps’, are detected within the Hα spatial emission which extends over 6–10 kpc in four galaxies, resolved compact emission (r < 3 kpc) is detected in five galaxies and extended regions of Hα emission are observed in the remaining four galaxies. We discuss these data in the context of different snapshots in a merger sequence and/or the evolutionary stages of coalescence of star-forming regions in an unstable disc. We find evidence of ordered orbital motion in galaxies as expected from disc models and the highest values of velocity dispersion (σ > 100 km s−1) in the most compact sources. This unique data set reveals that the most luminous star-forming galaxies at z > 1 are gaseous unstable discs indicating that a different mode of star formation could be feeding gas to galaxies at z > 1, and lending support to theories of cold dense gas flows from the intergalactic medium.