  The clustering properties of faint K<24 galaxies are measured in ultradeep J,
H and K near-IR images of the Hubble Deep Field South (HDF-S), obtained with
ISAAC at the VLT. A relatively large clustering amplitude is found up to K=24,
at a level comparable to the measurements at K~19. The redshift distribution of
K<24 galaxies extends to z_phot~4-5, and ~40% of the galaxies are at
z_phot>2.At the highest redshifts, 2<z_phot<4, galaxies selected in the rest
frame optical (K-band) appear more clustered than those selected in the rest
frame UV (i.e. Lyman Break Galaxies, LBGs). Galaxy clustering depends on the
J-K color at 2<z_phot<4. K-selected galaxies with J-K>1.7 reach r_0~8 h^-1 Mpc
comoving. This is a factor of 3--4 higher than the correlation length of LBGs
with similar number densities, down to V_606<27, and is also larger than the
correlation length of galaxies with blue J-K<1.7 colors. Hence at z about 3 a
color-density relation is observed which is similar to that observed locally.
Fluctuations in the amplitude of clustering due to cosmic variance may affect
our estimates derived from the small HDF-S field, but these are unlikely to
change our main conclusions. The galaxies with red J-K>1.7 colors at 2<z_phot<4
are likely older and more massive galaxies, on average, than LBGs. They were
presumably formed in the highest density perturbations at early epochs.
Semi-analytical hierarchical models do predict the existence of strongly
clustered populations at z~3, but with at least a factor of 10 lower number
density than the one measured. The overall properties of this strongly
clustered population consistently suggest that they are the progenitors, or
building blocks, of local massive early-type galaxies and z~1 EROs, close to
their major epochs of formation.
