A search in many small regions of the Crab Nebula has resulted in the detection of a small component of circular polarization. The variation of the sign and magnitude with position in the Nebula indicates that the polarization is of interstellar origin. On the basis of the polarity, strength, and colour dependence, it is concluded that the composition of the aligned grains causing this polarization is dielectric. Metallic particles are clearly ruled out. Some stars have also been observed with negative results.