  In the case of two-scalar field cosmology and, specifically for the Chiral
model, we determine an exact solution for the field equations with a
anisotropic background space. The exact solution can describe anisotropic
inflation with a Kantowski-Sachs geometry and it can be seen as the anisotropic
analogue of the hyperbolic inflation. Finally, we investigate the evolution for
the homogeneous perturbations around the new asymptotic solution.
