We present new results on the Ly \alpha emission-line kinematics of 18 z \sim 2 - 3 star-forming galaxies with multiple-peaked Ly \alpha profiles . With our large spectroscopic database of UV-selected star-forming galaxies at these redshifts , we have determined that \sim 30 \% of such objects with detectable Ly \alpha emission display multiple-peaked emission profiles . These profiles provide additional constraints on the escape of Ly \alpha photons due to the rich velocity structure in the emergent line . Despite recent advances in modeling the escape of Ly \alpha from star-forming galaxies at high redshifts , comparisons between models and data are often missing crucial observational information . Using Keck II NIRSPEC spectra of H \alpha ( z \sim 2 ) and [ OIII ] \lambda 5007 ( z \sim 3 ) , we have measured accurate systemic redshifts , rest-frame optical nebular velocity dispersions and emission-line fluxes for the objects in the sample . In addition , rest-frame UV luminosities and colors provide estimates of star-formation rates ( SFRs ) and the degree of dust extinction . In concert with the profile sub-structure , these measurements provide critical constraints on the geometry and kinematics of interstellar gas in high-redshift galaxies . Accurate systemic redshifts allow us to translate the multiple-peaked Ly \alpha profiles into velocity space , revealing that the majority ( 11/18 ) display double-peaked emission straddling the velocity-field zeropoint with stronger red-side emission . Interstellar absorption-line kinematics suggest the presence of large-scale outflows for the majority of objects in our sample , with an average measured interstellar absorption velocity offset of \langle \Delta v _ { abs } \rangle = -230 km s ^ { -1 } . A comparison of the interstellar absorption kinematics for objects with multiple- and single-peaked Ly \alpha profiles indicate that the multiple-peaked objects are characterized by significantly narrower absorption line widths . We compare our data with the predictions of simple models for outflowing and infalling gas distributions around high-redshift galaxies . While popular “ shell ” models provide a qualitative match with many of the observations of Ly \alpha emission , we find that in detail there are important discrepancies between the models and data , as well as problems with applying the framework of an expanding thin shell of gas to explain high-redshift galaxy spectra . Our data highlight these inconsistencies , as well as illuminating critical elements for success in future models of outflow and infall in high-redshift galaxies .