  Simulations of the formation of large-scale structure predict that dark
matter, low density highly ionized gas, and galaxies form 10 40 Mpc scale
filaments. These structure are easily recognized in the distribution of
galaxies, but have not been directly observed in the distribution of the gas.
We use Ly-alpha absorption lines in the spectra of 24 AGN to present a new way
to probe these filaments. We use a new catalogue of nearby (cz<10,000 km/s)
galaxies, complete down to a luminosity of about 0.05 L* for the region of
space analyzed here. Using HST spectra of 24 AGN we sample the gas associated
with a 30x5 Mpc galaxy filament at cz~3500 km/s. All of our sightlines pass
outside the virial radius of any known filament galaxy. Within 500 kpc of the
filament axis the detection rate is ~80%, while no detections are seen more
than 2.1 Mpc from the filament. The width of the Lya lines correlates with
filament impact parameter and the four BLAs in our sample all occur within 400
kpc of the filament axis, indicating increased temperature and/or turbulence.
Comparing to simulations, we find that the recent Haardt & Madau (2012)
extragalactic ionizing background predicts a factor 3-5 too few ionizing
photons. Using a more intense radiation field matches the hydrogen density
profile within 2.1 Mpc of the filament axis, but the simulations still
overpredict the detection rate between 2.1 and 5 Mpc from the axis.
