  Over the last few years, the Sloan Digital Sky Survey (SDSS) has discovered
several hundred quasars with redshift between 4.0 and 6.4. Including the
effects of magnification bias, one expects a priori that an appreciable
fraction of these objects are gravitationally lensed. We have used the Advanced
Camera for Surveys on the Hubble Space Telescope to carry out a snapshot
imaging survey of high-redshift SDSS quasars to search for gravitationally
split lenses. This paper, the first in a series reporting the results of the
survey, describes snapshot observations of four quasars at z = 5.74, 5.82, 5.99
and 6.30, respectively. We find that none of these objects has a lensed
companion within 5 magnitudes with a separation larger than 0.3 arcseconds;
within 2.5 magnitudes, we can rule out companions within 0.1 arcseconds. Based
on the non-detection of strong lensing in these four systems, we constrain the
z~6 luminosity function to a slope of beta>-4.63 (3 sigma), assuming a break in
the quasar luminosity function at M_{1450}^*=-24.0. We discuss the implications
of this constraint on the ionizing background due to quasars in the early
universe. Given that these quasars are not highly magnified, estimates of the
masses of their central engines by the Eddington argument must be taken
seriously, possibly challenging models of black hole formation.
