Polarization of the 100 micron thermal emission from 10 points in the Orion nebula has been measured. At one of the positions the degree, 5.7 percent, is the largest far-infrared polarization yet discovered. Except at a position in the barlike structure to the south, the position angles of the polarization vectors are well-ordered, suggesting that a uniform magnetic field threads the cloud. The magnetic field strength is estimated to be between 0.7 and 4 mG. The relationship of the degrees of polarization to the physical conditions in the cloud is discussed.