Intense effort has gone into the observation of optical, radio, and X-
ray gamma-ray burst (GRB) counterparts, either simultaneous to the bur
st or as quasi-steady lingering remnants. Here we report on a similar
study at higher energies of 250 GeV and above using ground-based teles
copes. The recent technical advances represented by the atmospheric Ch
erenkov imaging technique (Cawley & Weekes 1995) have opened up the fi
eld of gamma-ray astronomy above 250 GeV and raised the possibility th
at these techniques can be used with excellent fluence sensitivity in
exploring the GRB phenomenon. Observations by the Whipple collaboratio
n of nine BATSE positions, one acquired within 2 minutes of the report
ed BATSE burst time, using coordinates distributed through the BATSE C
oordinates Distribution Network (BACODINE) are reported. No evidence o
f TeV emission is found, and upper limits to the high-energy delayed o
r extended emission of observed candidates are calculated.