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 sa...