We present initial results from “ Via Lactea ” , the highest resolution simulation to date of Galactic CDM substructure . It follows the formation of a Milky Way-size halo with M _ { halo } = 1.8 \times 10 ^ { 12 } M _ { \odot } in a WMAP 3-year cosmology , using 234 million particles . Over 10,000 subhalos can be identified at z=0 : Their cumulative mass function is well-fit by N ( > M _ { sub } ) = 0.0064 ( M _ { sub } / M _ { halo } ) ^ { -1 } down to M _ { sub } = 4 \times 10 ^ { 6 } M _ { \odot } . The total mass fraction in subhalos is 5.3 % , while the fraction of surface mass density in substructure within a projected distance of 10 kpc from the halo center is 0.3 % . Because of the significant contribution from the smallest resolved subhalos , these fractions have not converged yet . Sub-substructure is apparent in all the larger satellites , and a few dark matter lumps are resolved even in the solar vicinity . The number of dark satellites with peak circular velocities above 10 { km s ^ { -1 } } ( 5 { km s ^ { -1 } } ) is 124 ( 812 ) : of these , 5 ( 26 ) are found within 0.1 r _ { vir } , a region that appeared practically smooth in previous simulations . The neutralino self-annihilation \gamma -ray emission from dark matter clumps is approximately constant per subhalo mass decade . Therefore , while in our run the contribution of substructure to the \gamma -ray luminosity of the Galactic halo amounts to only 40 % of the total spherically-averaged smooth signal , we expect this fraction to grow significantly as resolution is increased further . An all-sky map of the expected annihilation \gamma -ray flux reaching a fiducial observer at 8 kpc from the Galactic center shows that at the current resolution a small number of subhalos start to be bright enough to be visible against the background from the smooth density field surrounding the observer .