  In this paper we present an analysis of a chiral anisotropic cosmological
scenario from the perspective of quintom fields. In this setup quintessence and
phantom fields interact in a non-standard (chiral) way within an anisotropic
Bianchi type I background. We present our examination from two fronts:
classical and quantum approaches. In the classical program we find analytical
solutions given by a particular choice of the emerged relevant parameters.
Remarkably, we present an explanation of the ''big-bang'' singularity by means
of a ''big-bounce''. Moreover, isotropization is in fact reached as the time
evolves. On the quantum counterpart the Wheeler-DeWitt equation is analytically
solved for various instances given by the same parameter space from the
classical study, and we also include the factor ordering $\rm Q$. Having
solutions in this scheme we compute the probability density, which is in effect
damped as the volume function and the scalar fields evolve; and it also tends
towards a flat FLRW framework when the factor ordering constant $\rm Q \ll 0$.
This result might indicate that for a fixed set of parameters, the anisotropies
quantum-mechanically vanish for very small values of the parameter $\rm Q$.
Finally, classical and quantum solutions reduce to their flat FLRW counterparts
when the anisotropies vanish.
