Visiting Astronomer , W.M . Keck Telescope . The Keck Observatory is a joint facility of the University of California and the California Institute of Technology . We present the first results of an ongoing program to investigate the kinematic properties of high redshift damped Ly \alpha systems . Because damped Ly \alpha systems are widely believed to be the progenitors of current massive galaxies , an analysis of their kinematics allows a direct test of galaxy formation scenarios . Specifically , the kinematic history of protogalactic gas is a sensitive discriminator among competing theories of galaxy formation . We use the HIRES echelle spectrograph on the Keck 10 m telescope to obtain accurate , high-resolution spectra of 17 damped Ly \alpha systems . We focus on unsaturated , low-ion transitions such as Si II 1808 , since these accurately trace the velocity fields of the neutral gas dominating the baryonic content of the damped systems . The velocity profiles : ( 1 ) comprise multiple narrow components ; ( 2 ) are asymmetric in that the component with strongest absorption tends to lie at one edge of the profile ; and ( 3 ) exhibit a nearly uniform distribution of velocity widths between 20 and 200 km s ^ { -1 } . In order to explain these characteristics , we consider several physical models proposed to explain the damped Ly \alpha phenomenon , including rapidly rotating “ cold ” disks , slowly rotating “ hot ” disks , massive isothermal halos , and a hydrodynamic spherical accretion model . Using standard Monte Carlo techniques , we run sightlines through these model systems to derive simulated low-ion profiles . We develop four test statistics that focus on the symmetry and velocity widths of the profiles to distinguish among the models . Comparing the distributions of test statistics from the simulated profiles with those calculated from the observed profiles , we determine that the models in which the damped Ly \alpha gas is distributed in galactic halos and in spherically infalling gas , are ruled out at more than 99.9 \% confidence . A model in which dwarf galaxies are simulated by slowly rotating “ hot ” disks is ruled out at 97 \% confidence . More important , we demonstrate that the Cold Dark Matter Model , as developed by Kauffmann ( 1996 ) , is inconsistent with the damped Ly \alpha data at more than the 99.9 \% confidence level . This is because the CDM Model predicts the interception cross-section of damped Ly \alpha systems to be dominated by systems with rotation speeds too slow to be compatible with the data . This is an important result , because slow rotation speeds are generic traits of protogalaxies in most hierarchical cosmologies . We find that models with disks that rotate rapidly and are thick are the only tested models consistent with the data at high confidence levels . A Relative Likelihood Ratio Test indicates disks with rotation speeds , v _ { rot } < 180 km s ^ { -1 } , and scale heights , h < less than 0.1 times the radial scale length R _ { d } , are ruled out at the 99 \% confidence level . The most likely values of these parameters are v _ { rot } = 225 km s ^ { -1 } and h = 0.3 R _ { d } . We also find that these disks must be “ cold ” , since models in which \sigma _ { cc } / v _ { rot } > 0.1 are ruled out with 99 \% confidence , where \sigma _ { cc } is the velocity dispersion of the gas . We describe an independent test of the “ cold ” disk hypothesis . The test makes use of the redshift of emission lines sometimes detected in damped Ly \alpha systems , as well as the absorption profiles . The test potentially distinguishes among damped systems that are : ( 1 ) large rotating disks detected in absorption and emission , in which case a systematic relation exists between emission redshift and absorption velocity profile , and ( 2 ) emitting galaxies surrounded by satellite galaxies detected in damped Ly \alpha absorption , in which case the relation between emission and absorption redshifts is random . Finally we emphasize a dilemma stimulated by our findings . Specifically , while the kinematics of the damped Ly \alpha systems strongly favor a “ cold ” disk-like configuration , the low metallicities and type II Sn abundance patterns of damped Ly \alpha systems argue for a “ hot ” halo-like configuration . We speculate on how this dilemma might be resolved .