  We investigate the observational effects of a quintessence model in an
anisotropic spacetime. The anisotropic metric is a non-rotating particular case
of a generalized Godel's metric and is classified as Bianchi III. This metric
is an exact solution of the Einstein-Klein-Gordon field equations with an
anisotropic scalar field, which is responsible for the anisotropy of the
spacetime geometry. We test the model against observations of type Ia
supernovae, analyzing the SDSS dataset calibrated with the MLCS2k2 fitter, and
the results are compared to standard quintessence models with Ratra-Peebles
potentials. We obtain a good agreement with observations, with best values for
the matter and curvature density parameters $\Omega_M = 0.29$ and $\Omega_k=
0.01$ respectively. We conclude that present SNe Ia observations cannot, alone,
distinguish a possible anisotropic axis in the cosmos.
