A new electromagnetic shower detector will be constructed for the CLEO II experiment at CESR. It will consist of 8000 CsI(Tl) crystals coupled to solid state photodiodes. Extensive tests on the response of 175 CsI crystals are reported here. Each block measured 5 cm by 5 cm in cross section and 30 cm (16.2 radiation lengths) in depth. A fast and reliable method to determine acceptable light output and uniformity of crystals using a 137Cs radioactive source and photomultiplier readout was successfully developed. For test beam studies each crystal was equipped with four silicon photodiodes connected to a low-noise charge amplifier. Calibration with a positron test beam yielded average light output of 2500 photoelectrons per MeV and showed good correlation with the radioactive source exposures. In the beam tests at 180 (5000) MeV, energy resolutions of 4% (1.5%) and position resolutions transverse to the beam of 1.2 (0.3) cm were achieved. The effects of material between and in front of crystals, non-normal incidence, and staggering of adjacent crystals were studied, and together were found to degrade the energy resolution by only a modest amount. Operation of the system near room temperature will ensure low noise and stable response. The radiation sensitivity of a number of CsI blocks was measured and found to be acceptable for the radiation levels anticipated in CLEO II.