CUORE is a proposed tightly packed array of 1000 TeO₂ bolometers, each being a cube 5 cm on a side with a mass of 760 g: The array consists of 25 vertical towers, arranged in a square of 5 towers × 5 towers, each containing 10 layers of four crystals. The design of the detector is optimized for ultralow-background searches: for neutrinoless double-beta decay of ₁₃₀ Te (33.8% abundance), cold dark matter, solar axions, and rare nuclear decays. A preliminary experiment involving 20 crystals 3 × 3 × 6 cm³ of 340 g has been completed, and a single CUORE tower is being constructed as a smaller-scale experiment called CUORICINO. The expected performance and sensitivity, based on Monte Carlo simulations and extrapolations of present results, are reported.