Silicate dust in the interstellar medium is observed to be amorphous(1), yet silicate dust in comets(2,3) and interplanetary dust particles(4) is sometimes partially crystalline. The dust in young stars(5,6) also appears to be partially crystalline. These clouds to a planetary system, it must undergo some processing, Here we report observations of highly crystalline silicate dust in the disks surrounding binary red-giant stars. The dust was created in amorphous form in the outer atmospheres of the red giants, and therefore must be processed in the disks to become crystalline. The temperatures in these disks are too low for the grains to anneal; therefore, some low-temperature process must be responsible. As the physical properties of the disks around young stars and red giants are similar, our results suggest that low-temperature crystallization of silicate grains also can occur in protoplanetary systems.