A method for positioning a tool (24) on a tool chuck (20) employs a tool holding device (22, 50, 58), which includes a tool-accommodating area (32, 52, 66) for at least partly receiving the tool (24), a connecting area (26, 54 62) to be arranged on the tool chuck (20), and a positioning opening (48) through which a positioner (18) can be placed against the tool (24), which is located at least in part in the tool-accommodating area (32, 52, 66). The tool (24) is optically scanned to obtain a measurement. Subsequently, the tool holding device (22, 50, 58) is removed from the chuck (20), and the chuck is heated. Then, the tool (24), which is separated from the tool holding device (22, 50, 58), is shrink fitted in the chuck (20) at a position that is based on the measurement.