Over the last few years, the Sloan Digital Sky Survey (SDSS) hasdiscovered several hundred quasars with redshift between 4.0 and 6.4.Including the effects of magnification bias, one expects a priori thatan appreciable fraction of these objects are gravitationally lensed. Wehave used the Advanced Camera for Surveys on the Hubble Space Telescopeto carry out a snapshot imaging survey of high-redshift SDSS quasars tosearch for gravitationally split lenses. This paper, the first in aseries reporting the results of the survey, describes snapshotobservations 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 companionwithin 5 mag with a separation larger than 0.3" within 2.5 mag we canrule out companions within 0.1". Based on the nondetection of stronglensing in these four systems, we constrain the z~6 luminosity functionto a slope of β>-4.63 (3 σ), assuming a break in thequasar luminosity function at M*1450=-24.1. Wediscuss the implications of this constraint on the ionizing backgrounddue to quasars in the early universe. Given that these quasars are nothighly magnified, estimates of the masses of their central engines bythe Eddington argument must be taken seriously, possibly challengingmodels of black hole formation.