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We present spatially resolved dynamics for six strongly lensed star‐forming galaxies at   z = 1.7–3.1 , each enlarged by a linear magnification factor of  ∼ ×8 . Using the Keck laser guide star AO system and the OH‐Suppressing Infra‐Red Imaging Spectrograph integral field unit spectrograph, we resolve kinematic and morphological detail in our sample with an unprecedented fidelity, in some cases achieving spatial resolutions of ≃100 pc. With one exception our sources have diameters ranging from 1 to 7 kpc, integrated star formation rates of  2–40 M ⊙  yr −1   (uncorrected for extinction) and dynamical masses of  10 9.7−10.3  M ⊙  . With this exquisite resolution, we find that four of the six galaxies display coherent velocity fields consistent with a simple rotating disc model. Our model fits imply ratios for the systemic to random motion,   V c   sin  i /σ , ranging from 0.5 to 1.3 and Toomre disc parameters   Q  &lt; 1 . The large fraction of well‐ordered velocity fields in our sample is consistent with data analysed for larger, more luminous sources at this redshift. We demonstrate that the apparent contradiction with earlier dynamical results published for unlensed compact sources arises from the considerably improved spatial resolution and sampling uniquely provided by the combination of adaptive optics and strong gravitational lensing. Our high‐resolution data further reveal that all six galaxies contain multiple giant star‐forming H  ii  regions whose resolved diameters are in the range 300 pc to 1.0 kpc, consistent with the Jeans length expected in the case of dispersion support. From the kinematic data, we calculate that these regions have dynamical masses of  10 8.8−9.5  M ⊙  , also in agreement with local data. However, the density of star formation in these regions is  ∼100×  higher than observed in local spirals; such high values are only seen in the most luminous local starbursts. The global dynamics and demographics of star formation in these H  ii  regions suggest that vigorous star formation is primarily governed by gravitational instability in primitive rotating discs. The physical insight provided by the combination of adaptive optics and gravitational lensing suggests it will be highly valuable to locate many more strongly lensed distant galaxies with high star formation rates before the era of the next‐generation ground‐based telescopes when such observations will become routine.

Resolved spectroscopy of gravitationally lensed galaxies: recovering coherent velocity fields in subluminous z ∼ 2–3 galaxies