We report a dielectric constant of up to 5.4 x 10(5) at room temperature and 1 kHz for CaCu3Ti4O12 (CCTO) ceramics, derived from multiphase powders (coprecipitation products), made by a "chimie douce" (coprecipitation) method, and then sintered in air. The sintered products are pure-phase CCTO ceramics. The high dielectric constant is achieved by tuning the size of grains and the thickness of grain boundaries. The grain growth is controlled by varying the concentration of excess CuO in the initial powder (calcined coprecipitation products) between 1 and 3.1 wt%. The dielectric constant of pure CCTO ceramics increases with the initial CuO concentration, reaching its maximum at 2.4 wt% of CuO. A further increase of excess CuO in powders results in a permittivity decrease, accompanied by the formation of CuO as a separate phase in the sintered products. The unusual grain growth behavior is attributed to a eutectic reaction between CuO and TiO2 present in the initial powder.