Deep Imaging Search for Lyman-Alpha Emission Associated with an H i Cloud at Z = 3.4

We have carried out deep broad- and narrow-band imaging of a field reported to contain a possible Zel'dovich pancake at z = 3.4 in order to search for Lyα emission from galaxies or protogalaxies associated with the cloud. We are sensitive to objects with sizes less than 5" but do not detect any Lyα emission-line objects down to a limiting flux level of 3.8 x 10^-30^ ergs s^-1^ cm^2^ Hz^-1^, or an integrated line flux of 4.4 x 10^-17^ ergs s^-1^ cm^-2^. This limit is some 25 to 50 times fainter than the Lyα emission detected from a nearby radio galaxy at the same redshift.