  Optical images of SN 1987A show a triple ring structure. The inner (dust)
ring has recently increased in brightness and in the number of hot spots
suggesting that the supernova shock wave has collided with the dense
pre-existing circumstellar medium, a scenario supported by radio and X-ray
observations. Such a shocked environment is widely expected to result in the
acceleration of charged particles, and the accompanying emission of very high
energy gamma-rays. Here, we report the results of observations made in 2004 and
2006 which yield upper limits on the TeV gamma-ray flux, which are compared
with a theoretical prediction. In addition, we set upper limits on the TeV flux
for four high energy objects which are located within the same field of view of
the observation: the super-bubble 30 Dor C, the Crab-like pulsar PSR
B0540$-$69, the X-ray binary LMC X-1, and the supernova remnant N157B.
