We present high spatial-resolution ( \approx 2 kpc ) Atacama Large Millimeter/submillimeter Array ( ALMA ) observations of [ C ii ] 158 \mu m and dust-continuum emission from a galaxy at z = 3.7978 selected by its strong H i absorption ( a damped Ly \alpha absorber , DLA ) against a background QSO . Our ALMA images reveal a pair of star-forming galaxies separated by \approx 6 kpc ( projected ) undergoing a major merger . Between these galaxies is a third emission component with highly elevated ( 2 \times ) [ C ii ] 158 \mu m emission relative to the dust continuum , which is likely to arise from stripped gas associated with the merger . This merger of two otherwise-normal galaxies is not accompanied by enhanced star-formation , contrary to mergers detected in most luminosity-selected samples . The DLA associated with the merger exhibits extreme kinematics , with a velocity width for the low-ionization metal lines of \Delta v _ { 90 } \approx 470 km s ^ { -1 } , that spans the velocity spread revealed in the [ C ii ] 158 \mu m emission . We propose that DLAs with high \Delta v _ { 90 } values are a signpost of major mergers in normal galaxies at high redshifts , and use the distribution of the velocity widths of metal lines in high- z DLAs to provide a rough estimate the fraction of z > 3 galaxies that are undergoing a major merger .