In October 1987, three labs (Radiocarbon Accelerator Unit at Oxford University, University of Arizona in Tucson, Federal Institute of Technology in Zurich) out of a group of seven were chosen to use accelerator mass spectrometry to produce radiocarbon data on the Shroud of Turin. The article, written on the eve of the official announcement of the results, contains a description of the testing process and a short explanation of the steps taken to insure honest results. -- AATA