  We investigate the sky distribution of z ~ 6 Lyman break galaxies selected as
i'-dropouts having i' - z' > 1.45 down to z' < 26.5 in the Subaru Deep Field
(SDF). We discover 37 i'-dropouts clustered in a projected comoving 21.6 x 21.6
Mpc^2 region at z = 6, showing a local density excess. Carrying out follow-up
spectroscopy, we identify four of them as Lyman-alpha emitters at z = 5.92,
6.01, 6.03 and 6.03 (spread over a distance of 46.6 Mpc). The number density of
the cluster itself in SDF is ~ 2.2 x 10^{-7} Mpc^{-3}, smaller than those of
protoclusters (i.e., forming galaxy clusters) at z ~ 2-5.7. Also, the structure
shows ~4-21 times larger galaxy number density than those of z ~ 6 galaxies in
a general field. It has a mass of M ~ 1.5^{+1.8}_{-0.5} x 10^{15}M_sun,
comparable to those of z ~ 0-5 protoclusters. Since the contamination of our
sample by interlopers is estimated to be quite low, 5.9%, most of the other
unconfirmed i'-dropouts in the overdense region can be also z ~ 6 galaxies.
Hence, it could be a candidate forming cluster at z ~ 6, representing a
progenitor of galaxy clusters seen in the recent-day Universe.
