  We investigate the integrability of an anisotropic universe with matter and
cosmological constant formulated as Bianchi IX models. The presence of the
cosmological constant causes the existence of a critical point in the finite
part of the phase space. The separatrix associated to this Einstein's static
universe is entirely contained in an invariant isotropic plane forgetting the
singularity at the origin. This invariant plane of isotropy is an integrable
sub-space of the Taub type. In this paper we analyse the differential Galois
group of the second order variational equations to this plane in order to apply
the integrability theorem of the second author with Ramis and Sim\' o. The main
result is that the model is non-integrable by meromorphic functions.
