In earlier work we calculated the wavefunction and energy of the solvated polaron in DNA with a simple model in which the charge was taken to be on a single chain of bases at the center of the double helix. To better approximate the actual situation, we have now extended the calculations to the case in which the charge is distributed on two chains of bases, complementary to each other, one on each side of the center. The binding energy of the resulting polaron is somewhat larger than that obtained for the single-chain polaron, the result of each chain of the polaron being closer to some of the polarization charge it induces. Carrying out the calculations for a number of different sequences, we find that the polaron wavefunction is predominantly on one of the two chains, this usually being the one on which the charge was originally placed, despite the availability of lower energy sites on the other chain. This finding is in agreement with recent experiments of Schuster's group(Joy, A.; Ghosh, A. K.; Schuster, G. B. J. Am. Chem. Soc. 2006, 128, 5346-5347). Thus, in contradiction to the ideas of many researchers, there is no transport in which a hole zigzags from one chain to the other, as has been suggested for a sequence of guanines and cytosines (GCGCGC....), for example.