  The localization of vector multiplets is examined using the {\cal N}=1
supersymmetric U(1) gauge theory with the Fayet-Iliopoulos term coupled to
charged chiral multiplets in four dimensions. The vector field becomes
localized on a BPS wall connecting two different vacua that break the gauge
symmetry. The vacuum expectation values of charged fields vanish
(approximately) around the center of the wall, causing the Higgs mechanism to
be ineffective. The mass of the localized vector multiplet is found to be the
inverse width of the wall. The model gives an explicit example of this general
phenomenon. A five-dimensional version of the model can also be constructed if
we abandon supersymmetry.
