The natural remanent magnetization (NRM) carried by a centimeter-sized dark inclusion, the surrounding matrix, and individual chondrules in Allende was measured to determine the magnetic history of the meteorite. It was found that before demagnetization all the bulk specimens (matrix and the inclusion) have roughly the same NRM directions. There are, however, significant differences in direction between the inclusion and three separate regions of the surrounding matrix. It was also found that in one region the matrix had a systematic variation in NRM directions. The NRM directions of individual chondrules are scattered but they are grouped in one quadrant, with a mean direction different from that of the matrix. Stepwise thermal demagnetization revealed that all specimens carry two components of magnetization. The lower temperature component appears to be carried by pyrrhotite. The directions of the high-temperature component of NRM in both chondrules and bulk matrix specimens are almost randomly scattered. It is difficult to explain all the observed features of the NRM, but the following conditions appear to be required: (1) Chondrules and the inclusion were magnetized before accretion of Allende, hence they carry the record of early solar system magnetic fields. (2) The whole rock was partially remagnetized after accretion by a thermochemical event, thus carrying a record of a magnetic field that was present during or after accretion. (3) The bulk matrix, the inclusion, and some of the chondrules have rotated (or were deformed) after they were remagnetized.