Magnetic resonance electrical impedance tomography (MREIT) enables us to perform high-resolution conductivity imaging of an electrically conducting object. Injecting low-frequency current through a pair of surface electrodes, we measure an induced magnetic flux density using an MRI scanner and this requires a sophisticated MR phase imaging method. Applying a conductivity image reconstruction algorithm to measured magnetic flux density data subject to multiple injection currents, we can produce multi-slice cross-sectional conductivity images. When there exists a local region of fat, the well-known chemical shift phenomenon produces misalignments of pixels in MR images. This may result in artifacts in magnetic flux density image and consequently in conductivity image. In this paper, we investigate chemical shift artifact correction in MREIT based on the well-known three-point Dixon technique. The major difference is in the fact that we must focus on the phase image in MREIT. Using three Dixon data sets, we explain how to calculate a magnetic flux density image without chemical shift artifact. We test the correction method through imaging experiments of a cheese phantom and postmortem canine head. Experimental results clearly show that the method effectively eliminates artifacts related with the chemical shift phenomenon in a reconstructed conductivity image.