  Recently, gamma-ray emission at TeV energies has been detected from the
starburst galaxies NGC253 (Acero et al., 2009) and M82 (Acciari et al., 2009.
It has been claimed that pion production due to cosmic rays accelerated in
supernova remnants interacting with the interstellar gas is responsible for the
observed gamma rays. Here, we show that the gamma-ray pulsar wind nebulae left
behind by the supernovae contribute to the TeV luminosity in a major way. A
single pulsar wind nebula produces about ten times the total luminosity of the
Sun at energies above 1 TeV during a lifetime of 10^5 years. A large number of
3x10^4 pulsar wind nebulae expected in a typical starburst galaxy at a distance
of 4 Mpc can readily produce the observed TeV gamma rays.
