We present high resolution near-infrared spectra of \beta  Pictoris - a nearby young star with a debris disk . Fundamental low-J CO absorption lines are detected and strict upper limits are placed on the flux of v=2-1 low-J CO emission lines . The limit on the UV fluorescent emission flux in the v=2-1 lines is used to place a tight constraint on the inner extent of the CO gas . Assuming H i is the primary collision partner , the subthermal population of the low-J v=0 rotational levels constrains the density of the gas in the disk to n _ { H } = ( 2.5 ^ { +7.1 } _ { -1.2 } ) \times 10 ^ { 5 }  cm ^ { -3 } . If the distribution of hydrogen follows that of the other metals in the disk , we find that the mass of the gas in the disk is ( 0.17 ^ { +0.47 } _ { -0.08 } ) M _ { \earth } . We compare this mass to the gas mass necessary to brake the metals in the disk through ion-neutral reactions .