  The first image of a Cosmic Web, Lyman Limit System has just been made in HI
emission within the Local Group filament connecting M31 and M33. The
corresponding HI distribution function is in very good agreement with that of
the QSO absorption lines, confirming the 30-fold increase in surface area
expected between 10^19 cm^-2 and 10^17 cm^-2. The critical observational
challenge is crossing the ``HI desert'', the range of log(N_HI) from about 19.5
down to 18, over which photo-ionization by the intergalactic radiation field
produces an exponential decline in the neutral fraction from essentially unity
down to a few percent. Nature is kinder again to the HI observer below
log(N_HI) = 18, where the neutral fraction decreases only very slowly with
log(N_HI). Average spectra of the M31/M33 filament suggest a kinetic
temperature of 2x10^5 K for the parent ion population, consistent with
significant shock-heating. The brightest knot within the filament, with only a
2x10^4 K apparent temperature, is suggestive of localized cooling and
condensation. We have initiated two complimentary surveys that should lay the
groundwork for a comprehensive study of the Cosmic Web phenomenon in HI
emission. When combined with targeted optical and UV absorption line
observations, the total baryonic masses and enrichment histories of the Cosmic
Web could be determined over the complete range of environmental
over-densities.
