  In this paper we study an anisotropic model generated from a particular
Bianchi type-III metric, which is a generalization of G\"odel's metric and an
exact solution of Einstein's field equations. We analyse type Ia supernova
data, namely the SDSS sample calibrated with the MLCS2k2 fitter, and we verify
in which ranges of distances and redshifts the anisotropy could be observed. We
also consider, in a joint analysis, the position of the first peak in the CMB
anisotropy spectrum, as well as current observational constraints on the Hubble
constant. We conclude that a small anisotropy is permitted by the data, and
that more accurate measurements of supernova distances above z = 2 might
indicate the existence of such anisotropy in the universe.
