In order to achieve the high brightness promised by the single-pass Free Electron Laser (FEL) at the TESLA Test Facility (TTF) at DESY, the electron beam position must be controlled better than 10 μm over a distance of 15 m. The design of a monitor system with this accuracy is described. The silicon pixel detector, which is critical to this monitor, must have a position resolution of 1 μ m and an excellent sensitivity for soft X-rays above 150 eV. The silicon pixel detector and its readout electronics are also described.