  We propose a new model for the dark matter halo of the Milky Way that fits
the properties of the stellar stream associated with the Sagittarius dwarf
galaxy. Our dark halo is oblate with q_z = 0.9 for r < 10 kpc, and can be made
to follow the Law & Majewski model at larger radii. However, we find that the
dynamical perturbations induced by the Large Magellanic Cloud on the orbit of
Sgr cannot be neglected when modeling its streams. When taken into account,
this leads us to constrain the Galaxy's outer halo shape to have minor-to-major
axis ratio (c/a)_\Phi = 0.8 and intermediate-to-major axis ratio (b/a)_\Phi =
0.9, in good agreement with cosmological expectations.
