  We investigate the X-ray properties of the K-band-selected galaxies at
redshift 2 < z < 4 by using our deep near-infrared images obtained in the
MOIRCS Deep Survey project and the published Chandra X-ray source catalog. 61
X-ray sources with the 2-10 keV luminosity L_X = 10^{42}-10^{44} erg/s are
identified with the K-selected galaxies and we found that they are exclusively
(90%) associated with the massive objects with stellar mass larger than
10^{10.5} Msun. Our results are consistent with the idea that the M_BH/M_str
ratio of the galaxies at z=2-4 is similar to the present-day value. On the
other hand, the AGN detection rate among the very massive galaxies with the
stellar mass larger than 10^{11} Msun is high, 33% (26/78). They are active
objects in the sense that the black-hole mass accretion rate is ~ 1-50% of the
Eddington limit if they indeed have similar M_BH/M_str ratio with those
observed in the local universe. The active duration in the AGN duty cycle of
the high-redshift massive galaxies seems large.
