The Alpha Magnetic Spectrometer in a precursor version (AMS-01), was flown in June 1998 on a 51.6 degrees orbit and at altitudes ranging between 320 and 390 km, on board of the space shuttle Discovery (flight STS-91). AMS-01 included an Aerogel Threshold Cherenkov counter (ATC) to separate antiprotons from electrons and positrons from protons, for momenta below 3.5 GeV/c. This paper presents a description of the ATC counter and reports on its performances during the flight STS-91.