The L4 and L5 points of the Earth-Sun system were imaged using the University of Hawaii 2.24-m telescope on 1994 May 5-7 and July 6-8 UT. We used a thinned Tektronix 2048 × 2048 CCD, subtending a field 7.5 arcmin on a side. Our objective in this search was to locate sub-kilometer-sized asteroids orbiting near the libration point or, failing this, to set a rough upper limit on the number density of objects contained in such a population. Previous searches of these areas have used various less sensitive photographic techniques, but no asteroids have ever been discovered at the L4 or L5 points of the Earth-Sun system. The limiting sensitivity of this search wasR∼ 22.8, corresponding to C-type asteroids ∼350 m in diameter or S-type asteroids ∼175 m in diameter. No objects were discovered in the approximately 0.35 square degrees covered, leading to our crude estimate that the upper limit for the number density of objects at or above our detection threshold is approximately 3 objects per square degree. In this paper, we discuss the various considerations governing our search strategy. We also discuss the relevence of this search technique in looking for near-Earth asteroids in general. Finally, in this paper we point out areas of future theoretical work that can yield important information on Earth's libration regions, and we discuss the outlook for using large mosaic arrays in future asteroid searches of this nature.