Refractometric features of dual-core transversally chirped microstructured optical fibers (MOF) are evaluated. It is shown from numerical results that the chirped MOF could act as a structure with decoupled cores, forming a MachZehnder interferometer in which the analyte directly modulates the device transmittance by its differential influence on the effective refractive index of each core mode. We investigate the influence of the MOF parameters and the analyte refractive index on sensor performance. This novel structure is suitable for measuring refractive indices in the 1.33-1.44 range.