Chemical shift depends on the nucleus and its environment and is defined as nuclear shielding / applied magnetic field. Nuclei are shielded by a small magnetic field caused by circulating electrons, termed nuclear shielding. The strength of the shield depends on the different molecular environment in that the nucleus is embedded. Nuclear shielding is the difference between the magnetic field at the nucleus and the applied magnetic field.
Chemical shift is measured in parts per million (ppm) of the resonance frequency relative to another or a standard resonance frequency.
The major part of the MR signal comes from hydrogen protons; lipid protons contribute a minor part. The chemical shift between water and fat nuclei is about 3.5 ppm (~220 Hz; 1.5T). Through this difference in resonance frequency between water and fat protons at the same location, a misregistration (dislocation) by the Fourier Transformation take place, when converting MR signals from frequency to spatial domain. This effect is called chemical shift artifact or chemical shift misregistration artifact.

(CSI) Chemical shift imaging is an extension of MR spectroscopy, allowing metabolite information to be measured in an extended region and to add the chemical analysis of body tissues to the potential clinical utility of Magnetic Resonance. The spatial location is phase encoded and a spectrum is recorded at each phase encoding step to allow the spectra acquisition in a number of volumes covering the whole sample. CSI provides mapping of chemical shifts, analog to individual spectral lines or groups of lines.
Spatial resolution can be in one, two or three dimensions, but with long acquisition times od full 3D CSI. Commonly a slice-selected 2D acquisition is used. The chemical composition of each voxel is represented by spectra, or as an image in which the signal intensity depends on the concentration of an individual metabolite. Alternatively frequency-selective pulses excite only a single spectral component.
There are several methods of performing chemical shift imaging, e.g. the inversion recovery method, chemical shift selective imaging sequence, chemical shift insensitive slice selective RF pulse, the saturation method, spatial and chemical shift encoded excitation and quantitative chemical shift imaging.

See also Magnetic Resonance Spectroscopy.

Quick Overview
Please note that there are different common names for this artifact.

During frequency encoding, fat protons precess slower than water protons in the same slice because of their magnetic shielding. Through the difference in resonance frequency between water and fat, protons at the same location are misregistrated (dislocated) by the Fourier transformation, when converting MRI signals from frequency to spatial domain. This chemical shift misregistration cause accentuation of any fat-water interfaces along the frequency axis and may be mistaken for pathology. Where fat and water are in the same location, this artifact can be seen as a bright or dark band at the edge of the anatomy.
Protons in fat and water molecules are separated by a chemical shift of about 3.5 ppm. The actual shift in Hertz (Hz) depends on the magnetic field strength of the magnet being used. Higher field strength increases the misregistration, while in contrast a higher gradient strength has a positive effect. For a 0.3 T system operating at 12.8 MHz the shift will be 44.8 Hz compared with a 223.6 Hz shift for a 1.5 T system operating at 63.9 MHz.

For artifact reduction helps a smaller water fat shift (higher bandwidth), a higher matrix, an in phase TE or a spin echo technique. Since the misregistration offset is present in the read out axis the patient may be rescanned with this axis parallel to the fat-water interface. Steeper gradient may be employed to reduce the chemical shift offset in mm. Another strategy is to employ specialized pulse sequences such as fat saturation or inversion recovery imaging. Fat suppression techniques eliminate chemical shift artifacts caused by the lack of fat signal.

See also Black Boundary Artifact and Magnetic Resonance Spectroscopy.

A compound with respect to whose frequency the chemical shifts of other compounds can be compared. The standard can be either internal or external to the sample. Because of the need for possible corrections due to differential magnetic susceptibility between an external standard and the sample being measured, the use of an internal standard is generally preferred.

Image artifact of apparent spatial offset of regions with different chemical shifts along the direction of the frequency encoding gradient; a similar effect may be found in the slice selection direction.

See Chemical Shift Artifact.