We present high-resolution near-infrared spectra of β 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 Hi is the primary collision partner, the sub-thermal population of the low-J v = 0 rotational levels constrains the density of the gas in the disk to nH = (2.5+7.1 −1.2)×105 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 −0.08M⊕. We compare this mass to the gas mass necessary to brake the metals in the disk through ion–neutral reactions.