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We propose a new model for the dark matter halo of the Milky Way that fitsthe properties of the stellar stream associated with the Sagittarius dwarfgalaxy. Our dark halo is oblate with q_z = 0.9 for r < 10 kpc, and can be madeto follow the Law & Majewski model at larger radii. However, we find that thedynamical perturbations induced by the Large Magellanic Cloud on the orbit ofSgr 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-majoraxis ratio (c/a)_\Phi = 0.8 and intermediate-to-major axis ratio (b/a)_\Phi =0.9, in good agreement with cosmological expectations.

Constraints on the shape of the Milky Way dark matter halo from the Sagittarius stream