We present the SILVERRUSH program strategy and clustering properties investigated with \sim 2 , 000 Ly \alpha emitters at z = 5.7 and 6.6 found in the early data of the Hyper Suprime-Cam ( HSC ) Subaru Strategic Program survey exploiting the carefully designed narrowband filters . We derive angular correlation functions with the unprecedentedly large samples of LAEs at z = 6 - 7 over the large total area of 14 - 21 deg ^ { 2 } corresponding to 0.3 - 0.5 comoving Gpc ^ { 2 } . We obtain the average large-scale bias values of b _ { avg } = 4.1 \pm 0.2 ( 4.5 \pm 0.6 ) at z = 5.7 ( z = 6.6 ) for \gtrsim L ^ { * } LAEs , indicating the weak evolution of LAE clustering from z = 5.7 to 6.6 . We compare the LAE clustering results with two independent theoretical models that suggest an increase of an LAE clustering signal by the patchy ionized bubbles at the epoch of reionization ( EoR ) , and estimate the neutral hydrogen fraction to be x _ { HI } = 0.15 ^ { +0.15 } _ { -0.15 } at z = 6.6 . Based on the halo occupation distribution models , we find that the \gtrsim L ^ { * } LAEs are hosted by the dark-matter halos with the average mass of \log ( \left < M _ { h } \right > / M _ { \odot } ) = 11.1 ^ { +0.2 } _ { -0.4 } ( 10.8 ^ { +0.3 } _ { -0.5 } ) at z = 5.7 ( 6.6 ) with a Ly \alpha duty cycle of 1 % or less , where the results of z = 6.6 LAEs may be slightly biased , due to the increase of the clustering signal at the EoR . Our clustering analysis reveals the low-mass nature of \gtrsim L ^ { * } LAEs at z = 6 - 7 , and that these LAEs probably evolve into massive super- L ^ { * } galaxies in the present-day universe .