This paper describes the design, fabrication and testing of the Anti-Coincidence Detector (ACD) for the Gamma-ray Large Area Space Telescope (GLAST) Large Area Telescope (LAT). The ACD is LAT first-level defense against the charged cosmic ray background that outnumbers the gamma rays by 3-5 orders of magnitude. The ACD covers the top and 4 sides of the LAT tracking detector, requiring a total active area of ~8.3 square meters. The ACD detector utilizes plastic scintillator tiles with wave-length shifting fiber readout. In order to suppress self-veto by shower particles at high gamma-ray energies, the ACD is segmented into 89 tiles of different sizes. The overall ACD efficiency for detection of singly charged relativistic particles entering the tracking detector from the top or sides of the LAT exceeds the required 0.9997.