The PAMELA space experiment [4] will be launched on-board of a polarorbiting Resurs DK1 satellite in 2004. The primary objective of PAMELA is to measure the flux of antiprotons (80 MeV 190 GeV) and positrons (50 MeV 270 GeV) in the cosmic radiation. PAMELA is built around a permanent magnet silicon spectrometer which is surrounded by an anticounter system. The anticounter system uses sheets of plastic scintillator to identify particles which do not pass cleanly through the acceptance of the spectrometer but still give rise to coincidental energy deposits in the time-of-flight / trigger scintillators positioned at the entrance and exit of the spectrometer. The construction of the anticounter system is described in detail along with the custom read-out, data acquisition and calibration electronics. Results from qualification studies are also discussed.