We present a sensing architecture consisting of a two-core chirped microstructured optical fiber (MOF) for refractive index sensing of fluids. We show that by introducing a chirp in the hole size, the MOF can be a structure with decoupled cores, forming a Mach-Zehnder interferometer in which the analyte directly modulates the device transmittance by its differential influence on the effective refractive index of each core mode. We show that by filling all fiber holes with analyte, the sensing structure achieves high sensitivity (transmittance changes of 300 per RIU at 1.42) and has the potential for use over a wide range of analyte refractive index.