A milliarcsecond x-ray telescope can image stars and can observe galaxies with resolution matching radio astronomy--opening the door to fundamental discoveries. The convenient milliarcsecond x-ray optic is a paraboloid mirror with a graze angle close to half degree and with 0.1 arc sec tolerance. For a reasonable plate scale, the cross sectional radius of the paraboloid should be about 5 - 10 meters. The glass substrate, looking near cylindrical, is prepared by cementing together 36 segments of 10 degree each. This is placed in the machine with its axis horizontal. Accurate positioning of the substrate is possible, using positron sensors and positioning pads at 5 locations. The substrate is supported all along its circumference, to compensate for the gravity effects. Along the axis, the focus point of the desired paraboloid is rigidly located for regular use throughout the prolonged period of mirror making. By 4 carefully chosen random motions of the tool and the substrate, it is possible to derive the desired paraboloid surface. The image at the focus is used to test the surface errors. For this, a test-parallel beam of light is generated using the same paraboloid mirror in combination with a flat reflector. At the end, the glass substrate is transformed into a vacuum chamber, and a multi-layer, thin film coating is deposited on the mirror surface.