We use chiral symmetry to calculate the very long distance contributions to the KL - KS mass difference. We determine that the dominant effect arises from the two-pion dispersive contribution, which by itself produces a large result comparable to or greater than the experimental mass difference (with the correct sign). Some contributions from intermediate distance are also estimated and could be significant. These conclusions reinforce the need, first pointed out by Wolfenstein, to include an additive parameter to account for the long distance contributions in phenomenological studies of the KL - KS mass difference. The parameter may be determined from the data if the B-meson lifetime is as large as recent experiments indicate.