Centaurus X-3 is a well-studied high-mass accreting X-ray binary and a variable source of high energy gamma rays with energies from 100 MeV to 1 TeV. Previous results have suggested that the origin of the gamma rays is not the immediate vicinity of the neutron star but is sited in the accretion disc, perhaps in an accretion wake. The Durham Mark 6 gamma ray telescope has been used to measure the gamma ray flux from Centaurus X-3 with much higher sensitivity than previous ground-based measurements. The flux above ~ 400 GeV was measured to be (2 +/- 0.3) x 10^-11 cm^-2 s^-1 and appears constant over a period of 2 - 3 months. In 10 hours of observations there is no evidence for periodicity in the detected gamma rays at the X-ray spin period either from a site in the region of the neutron star, or from any other potential site in the orbit.