  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 \ion{H}{1} 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 $n_{\rm H} = (2.5^{+7.1}_{-1.2})\times10^5$ 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.
