  Muon spin rotation and relaxation experiments on the centrosymmetric
intermetallic superconductor LaNiGa$_2$ are reported. The appearance of
spontaneous magnetic fields coincides with the onset of superconductivity,
implying that the superconducting state breaks time reversal symmetry,
similarly to non-centrosymmetric LaNiC$_2$. Only four triplet states are
compatible with this observation, all of which are non-unitary triplets. This
suggests that LaNiGa$_2$ is the centrosymmetric analogue of LaNiC$_2$. We argue
that these materials are representatives of a new family of paramagnetic
non-unitary superconductors.
