  We introduce the largest to date survey of massive quiescent galaxies at
redshift z~1.6. With these data, which cover 27.6 deg^2, we can find
significant numbers of very rare objects such as ultra-massive quiescent
galaxies that populate the extreme massive end of the galaxy mass function, or
dense environments that are likely to become present-day massive galaxy
clusters. In this paper, the first in a series, we apply our gzK adaptation of
the BzK technique to select our z~1.6 galaxy catalog and then study the
quiescent galaxy stellar mass function with good statistics over M_stars ~
10^10.2 - 10^11.7 M_sun --- a factor of 30 in mass --- including 60
ultra-massive z~1.6 quiescent galaxies with M_stars > 10^11.5 M_sun. We find
that the stellar mass function of quiescent galaxies at z~1.6 is well
represented by the Schechter function over this large mass range. This suggests
that the mass quenching mechanism observed at lower redshifts must have already
been well established by this epoch, and that it is likely due to a single
physical mechanism over a wide range of mass. This close adherence to the
Schechter shape also suggests that neither merging nor gravitational lensing
significantly affect the observed quenched population. Finally, comparing
measurements of M* parameters for quiescent and star-forming populations (ours
and from the literature), we find hints of an offset (M*_SF > M*_PE), that
could suggest that the efficiency of the quenching process evolves with time.
