Planet formation is believed to occur in the disks of gas and dust that surround young solar-type stars1. Most stars, however, form in multiple systems2,3,4,5, where the presence of a close companion could affect the structure of the disk6,7,8 and perhaps interfere with planet formation. It has been difficult to investigate this because of the resolution needed. Here we report interferometric observations (at a wavelength of 7 mm) of the core of the star-forming region L1551. We have achieved a linear resolution of seven astronomical units (less than the diameter of Jupiter's orbit). The core of L1551 contains two distinct disks, with a separation of 45 AU; these appear to be associated with a binary system. Both disks are spatially resolved, with semi-major axes of about 10 AU, which is about a factor of ten smaller than disks around isolated stars9,10,11,12. The disk masses are of order 0.05 solar masses, which could be enough to form planetary systems like our own.