We present early results from an ongoing study of the kinematic structure of star-forming galaxies at redshift z \sim 2 - 3 using integral-field spectroscopy of rest-frame optical nebular emission lines in combination with Keck laser guide star adaptive optics ( LGSAO ) . We show kinematic maps of 3 target galaxies Q1623-BX453 , Q0449-BX93 , and DSF2237a-C2 located at redshifts z = 2.1820 , 2.0067 , and 3.3172 respectively , each of which is well-resolved with a PSF measuring approximately 0.11 - 0.15 arcsec ( \sim 900 - 1200 pc at z \sim 2 - 3 ) after cosmetic smoothing . Neither galaxy at z \sim 2 exhibits substantial kinematic structure on scales \gtrsim 30 km s ^ { -1 } ; both are instead consistent with largely dispersion-dominated velocity fields with \sigma \sim 80 km s ^ { -1 } along any given line of sight into the galaxy . While the primary emission component of Q0449-BX93 shows no spatially-resolved kinematic structure , a faint , kinematically distinct emission region is superposed on the primary region at a relative velocity of \sim 180 km s ^ { -1 } , suggesting the possible presence of a merging satellite galaxy . In contrast , DSF2237a-C2 presents a well-resolved gradient in velocity over a distance of \sim 4 kpc with peak-to-peak amplitude of 140 km s ^ { -1 } . This velocity shear was previously undetected in seeing-limited long-slit observations despite serendipitous alignment of the slit with the kinematic major axis , highlighting the importance of LGSAO for understanding velocity structure on subarcsecond scales . It is unlikely that DSF2237a-C2 represents a dynamically cold rotating disk of ionized gas as the local velocity dispersion of the galaxy ( \sigma = 79 km s ^ { -1 } ) is comparable to the observed shear . Using extant multi-wavelength spectroscopy and photometry we relate these kinematic data to physical properties such as stellar mass , gas fraction , star formation rate , and outflow kinematics and consider the applicability of current galaxy formation models . While some gas cooling models reproduce the observed kinematics better than a simple rotating disk model , even these provide a poor overall description of the target galaxies , suggesting that our current understanding of gas cooling mechanisms in galaxies in the early universe is ( at best ) incomplete .