One of the foremost goals in the study of cosmological reionization is understanding the nature of the sources of the ionizing photons. The search for leaking ionizing radiation from high-redshift star-forming galaxies has resulted in dozens of promising candidates, yet few confirmed detections. In this thesis, I present results from a survey for z~2.85 ionizing Lyman-Continuum (LyC) emission in the HS1549+1933 field and place constraints on the amount of ionizing radiation escaping from star-forming galaxies. Using a custom narrowband filter (NB3420) tuned to wavelengths just below the Lyman limit at z>=2.82, I probe the LyC spectral region of 49 Lyman break galaxies (LBGs) and 91 Lyman-alpha emitters (LAEs) spectroscopically confirmed at z>=2.82. I also present high-resolution, UVJH follow-up HST observations of 16 z~3 candidate LyC emitters identified with the NB3420 filter. With these follow-up data, I obtain high spatial-resolution photometric redshifts of all subarcsecond components of the high-redshift galaxies in order to eliminate foreground contamination and identify robust candidates for leaking LyC emission. I find only one object with a robust LyC detection that is not due to foreground contamination. A comparison with representative samples of LBGs indicates that the most exceptional aspect of the stellar population fit to this object is its young age (<50 Myr). I obtain a contamination-free estimate for the comoving specific ionizing emissivity at z=2.85, indicating (with large uncertainties) that star-forming galaxies provide roughly the same contribution as QSOs to the ionizing background at this redshift. The results of my thesis work show that foreground contamination prevents ground-based LyC studies from obtaining a full understanding of LyC emission from z~3 star-forming galaxies. Future progress in direct LyC searches is contingent upon the elimination foreground contaminants through high spatial-resolution observations, and upon acquisition of sufficiently deep LyC imaging to probe ionizing radiation in galaxies at the faint end of the luminosity function.