X-ray Absorption Near Edge Structure (XANES) imaging, an advanced absorption spectroscopy technique, at the Transmission X-ray Microscopy (TXM) Beamline X8C of NSLS enables high-resolution chemical mapping (a.k.a. chemical composition identification or chemical spectra fitting). Two-Dimensional (2D) chemical mapping has been successfully applied to study many functional materials to decide the percentages of chemical components at each pixel position of the material images. In chemical mapping, the attenuation coefficient spectrum of the material (sample) can be fitted with the weighted sum of standard spectra of individual chemical compositions, where the weights are the percentages to be calculated. In this paper, we first implemented and compared two fitting approaches: (i) a brute force enumeration method, and (ii) a constrained least square minimization algorithm proposed by us. Next, as 2D spectra fitting can be conducted pixel by pixel, so theoretically, both methods can be implemented in parallel. In order to demonstrate the feasibility of parallel computing in the chemical mapping problem and investigate how much efficiency improvement can be achieved, we used the second approach as an example and implemented a parallel version for a multi-core computer cluster. Finally we used a novel way to visualize the calculated chemical compositions, by which domain scientists could grasp the percentage difference easily without looking into the real data.