An integrated optical Michelson interferometer in glass has been developed. Glass provides the advantage of having the same refractive index as fibers. Therefore, Fabry-Perot resonances due to Fresnel reflections are avoided at the fiber-chip connections. A symmetric coupler, which is the basic component in this Michelson configuration, was fabricated by a field assisted ion exchange of potassium in BK7 glass. The minimum interguide separation of the coupled arms was 7 um, and the waveguide width was 3 um for single-mode operation at 633 nm. Light of the single mode input fiber is devided by the symmetric coupler into two beams. One coupler arm, which works as the reference arm, is terminated by a mirror on the end-surface of the substrate. At the end of the other arm, which represents the sensing arm, a quarter pitch GRIN-lens with an antireflective coating collimates the outcoming light. A moving mirror mounted on a piezotranslator reflects the light into the GRIN-lens and the symmetric coupler recombines the sensing and the reference beam. A change in optical path length is converted to an intensity signal by the coupler. The distance between two peaks of the interference signal pattern corresponds to a displacement of half wavelength. Experimental measurements using 633 nm wavelength show that the amplitude remains constant within 10 %, scanning a distance of 25 mm between the GRIN-lense and the mirror. A resolution below 1/100 wavelength can be achieved by single sideband detection using integrated thermooptic phase modulators.