The distribution of shapes of galaxies ’ dark halos provides a basic test for models of galaxy formation . To-date , few dark halo shapes have been measured , and the results of different methods appear contradictory . Here , we add to the sample of measured shapes by calculating the flattening of the Milky Way ’ s dark halo based on the manner in which the gas layer in the Galaxy flares with radius . We also test the validity of this technique – which has already been applied to several other galaxies – by comparing the inferred halo flattening to that obtained from a stellar-kinematic analysis , which can only be applied to the Milky Way . Both methods return consistent values for the shape of the Milky Way ’ s halo , with a shortest-to-longest axis ratio for the dark matter distribution of q = 0.75 \pm 0.25 . However , this consistency is only achieved if we adopt a value of R _ { 0 } = 7 \pm 1 { kpc } for the Sun ’ s distance to the Galactic center . Although this value is smaller than the IAU-sanctioned R _ { 0 } = 8.5 { kpc } , it is quite consistent with current observations . Whatever value of R _ { 0 } is adopted , neither method returns halo parameters consistent with a disk-like mass distribution , for which q \sim 0.2 . This finding rules out cold molecular gas and decaying massive neutrinos as dark matter candidates .