The determinations of many fundamental parameters of the Standard Model are hindered by the non-perturbative nature of QCD at low energies. The only known way to calculate quantities governed by QCD at these energies is the use of lattice field theory techniques. In particular, extremely precise measurements of DeltaMd, and recently of Delta Ms, exist. By combining these measurements with a comparably precise calculation of the hadronic matrix elements contributing to Delta Md and DeltaMs, the Unitarity Triangle would he much more tightly constrained, giving insights into new physics. Current lattice calculations of these matrix elements suffer from uncontrolled uncertainties. This report presents a calculation and results for the matrix elements relevant for the analysis of B0 -- B¯0 mixing using the Asqtad (light-quark) and Fermilab (heavy-quark) actions. The calculation is performed on the 2+1 MILC ensembles at three different lattice spacings, and uses staggered chiral perturbation theory to perform the extrapolations to the physical light quark masses as well as to the continuum. All known systematic errors are explored and estimated resulting in a value and uncertainty for xi that can be used directly as input for Unitarity constraints.