We experimentally observe the local Brillouin dynamic grating (BDG) based on a chaotic laser in a polarization-maintaining fiber for the first time, to the best of our knowledge. The grating length of the chaotic BDG can be adjusted by changing the optical spectral width of the chaotic laser. The characteristics of the reflection spectrum versus the grating length are further analyzed, which agrees with the theory of fiber Bragg grating. Temperature distributed measurements based on the chaotic BDG have been demonstrated with a spatial resolution of an order of centimeter.