In this paper, a novel chemical sensor is presented based on graphene deposited on the periodic pattern of the photonic crystal. The sensor structure is very simple to fabricate. Also, the proposed sensor thickness in the order of the nanometer makes it compact and suitable for integrating with optical equipment. The principle of sensing is based on the doping process of graphene due to the adsorption of the chemical molecules that serve as charge carriers. The sensor action under critical coupling results in generating the mid-infrared fano-resonance of the half-absorption band. Then, manipulating the graphene Fermi energy and geometrical parameters, a high quality factor can be attained in the resonance frequency that can provide the sensing possibility through the wavelength interrogation method. The results demonstrate that the proposed sensor can detect the chemicals with spectral shifts of 10 pm for steps of 5 charge carriers which is equal to a resolution smaller than 0.1ppm . Compared with other types of chemical graphene-based sensors employing optical fibers and plasmonic Fabry-Perot cavity, high resolution and sensitivity as well as the very simple geometry of the proposed sensing structure make it a promising candidate for ultra-sensitive chemical and biochemical detection.