We present Submillimeter Array¹The Submillimeter Array is a joint project between the Submillimeter Astrophysical Observatory and the Academica Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academica Sinica. observations of the 880 μm continuum emission from three circumstellar disks around young stars in Orion that lie several arcminutes ( 1 pc) north of the Trapezium cluster. Two of the three disks are in the binary system 253-1536. Silhouette disks 216-0939 and 253-1536a are found to be more massive than any previously observed Orion disks, with dust masses derived from their submillimeter emission of 0.045 M _☉ and 0.066 M _☉, respectively. The existence of these massive disks reveals that the disk mass distribution in Orion does extend to high masses, and that the truncation observed in the central Trapezium cluster is a result of photoevaporation due to the proximity of O-stars. 253-1536b has a disk mass of 0.018 M _☉, making the 253-1536 system the first optical binary in which each protoplanetary disk is massive enough to potentially form solar systems.