With the increasing use of charge-coupled devices for astronomical observations, it is vital to obtain the highest quantum efficiency possible due to the limited amount of observing time available on large telescopes. One method of increasing the response of back-illuminated CCDs is to apply antireflection coatings. Because silicon's index of refraction is extremely high in the ultra-violet, a gain of more than 100% in quantum efficiency can be achieved at a wavelength of 0.37 Am with the proper choice of dielectric thin-film materials. We present a study of materials suitable for silicon CCD antireflection coatings for use in the 0.32 to 1.0 Am spectral range. Constraints on these materials, such as refractive index, absorption coefficient, application method, tempera-ture requirements, internal stress, and radioactivity, are discussed. We find hafnium oxide, lead fluoride, and aluminum oxide to be among the most suitable thin-film materials available. We also present a number of single- and multiple-layer antireflection coating designs optimized for CCDs, with particular emphasis on the blue and ultraviolet.