  Most of the baryons in the local universe are ``missing'' in that they are
not in galaxies or in the previously detected gaseous phases. These missing
baryons are predicted to be in a moderately hot phase, 10^5-10^7 K, largely in
the form of giant cosmic filaments that connect the denser virialized clusters
and groups of galaxies. Models show that the highest covering fraction of such
filaments occurs in superclusters. To determine whether such filaments exist,
we have begun a project to search for UV absorption against AGNs projected
behind possible supercluster filaments. Using data from the HST and FUSE
archives along with new observations, we have detected UV absorption within
about 1300 km/s of seven supercluster sightlines out of a sample of eight. The
likelihood of such detections being generated by chance is less than 10^-4.
