Although atmospheric Cherenkov telescopes have restricted fields of view, their fluence sensitivity warrants a search for gamma-ray burst phenomena. A search for 400 GeV gamma-ray bursts on a 1 s time-scale using archival data taken between 1988 and 1992 with the Whipple Collaboration 10 m reflector is presented. No evidence of such bursts is found. Bursts of TeV gamma rays have been predicted from exotic astrophysical objects such as Primordial Black Holes and Cosmic Strings. An upper limit to the number density of exploding PBH of 3.0±1.0×10 6 pc -3 yr -1 is calculated.