An imaging calorimeter has been designed and is being built for the PAMELA satellite-borne experiment. The physics goals of the experiment are the measurement of the flux of antiprotons, positrons and light isotopes in the cosmic radiation. The calorimeter is designed to perform a precise measurement of the total energy deposited, to reconstruct the spatial development of the showers (both in the longitudinal and in the transverse directions), and to measure the energy distribution along the shower itself. From this information, the calorimeter will identify antiprotons from a electron background and positrons in a background of protons with an efficiency of about 95% and a rejection power better than 10^-4. Furthermore, a self-trigger system has been implemented with the calorimeter that will be employed to measure high-energy (from about 300 GeV to more than 1 TeV) electrons. The instrument is composed of 22 layers of tungsten, each sandwiched between two views of silicon strip detectors (X and Y). The signals are read out by a custom VLSI front-end chip, the CR1.4P, specifically designed for the PAMELA calorimeter, with a dynamic range of 7.14 pC or 1400 mip (minimum ionizing particle). We report on the simulated performance and prototype design.