Authors:Wilson et alAbstract:The young and nearby star \beta\ Pictoris (\beta\ Pic) is surrounded by a debris disk composed of dust and gas known to host a myriad evaporating exocomets, planetesimals and at least one planet. At an edge-on inclination, as seen from Earth, this system is ideal for debris disk studies providing an excellent opportunity to use absorption spectroscopy to study the planet forming environment. Using the Cosmic Origins Spectrograph (COS) instrument on the Hubble Space Telescope (HST) we observe the most abundant element in the disk, hydrogen, through the HI Lyman \alpha\ (Ly-\alpha\) line. We present a new technique to decrease the contamination of the Ly-\alpha\ line by geocoronal airglow in COS spectra. This Airglow Virtual Motion (AVM) technique allows us to shift the Ly-\alpha\ line of the astrophysical target away from the contaminating airglow emission revealing more of the astrophysical line profile. The column density of hydrogen in the \beta\ Pic stable gas disk at the stellar radial velocity is measured to be log(NH/1cm2)≪18.5. The Ly-\alpha\ emission line profile is found to be asymmetric and we propose that this is caused by HI falling in towards the star with a bulk radial velocity of 41±6 km/s relative to \beta\ Pic and a column density of log(NH/1cm2)=18.6±0.1. The high column density of hydrogen relative to the hydrogen content of CI chondrite meteorites indicates that the bulk of the hydrogen gas does not come from the dust in the disk. This column density reveals a hydrogen abundance much lower than solar, which excludes the possibility that the detected hydrogen could be a remnant of the protoplanetary disk or gas expelled by the star. We hypothesise that the hydrogen gas observed falling towards the star arises from the dissociation of water originating from evaporating exocomets.