We propose a biosensor based on the diffraction of Bloch surface waves (BSWs) in periodic dielectric stacks. Significant enhancement of diffraction efficiency by a biomolecule grating placed on the multilayer is predicted when a BSW is excited through a prism in the Kretschmann configuration. Numerical calculations for BSW in a Si/SiO(2) dielectric stack show an increase of diffraction intensity up to three orders of magnitude with respect to the case of surface plasmon wave enhancement. The mechanism that leads to large field confinement and the absence of absorption losses in the dielectric system make this solution flexible and suitable to different grating periods.