  Observations of the lengthy tidal streams produced by the destruction of the
Sagittarius dwarf spheroidal (Sgr dSph) are capable of providing strong
constraints on the shape of the Galactic gravitational potential. However,
previous work, based on modeling different stream properties in axisymmetric
Galactic models has yielded conflicting results: while the angular precession
of the Sgr leading arm is most consistent with a spherical or slightly oblate
halo, the radial velocities of stars in this arm are only reproduced by prolate
halo models. We demonstrate that this apparent paradox can be resolved by
instead adopting a triaxial potential. Our new Galactic halo model, which
simultaneously fits all well-established phase space constraints from the Sgr
stream, provides the first conclusive evidence for, and tentative measurement
of, triaxiality in an individual dark matter halo. The Milky Way halo within ~
60 kpc is best characterized by a minor/major axis ratio of the isovelocity
contours c/a ~ 0.67, intermediate/major axis ratio b/a ~ 0.83, and triaxiality
parameter T ~ 0.56. In this model, the minor axis of the dark halo is
coincident with the Galactic X axis connecting the Sun and the Galactic Center
to within ~ 15 degrees, while the major axis also lies in the Galactic plane,
approximately along the Galactic Y axis.
