We demonstrate experimentally an optical sensor based on a monolithically integrated Mach-Zehnder interferometer comprising a liquid-core waveguide in one of the optical paths. The device is fabricated with a technique for self-forming microchannels in silica-on-silicon using standard photolithography and deposition processes. Refractometry with a resolution of better than 4x10(-6) is demonstrated using the thermo-optic effect of the liquid medium to vary its refractive index. The polarization dependence of the device response is analyzed.