During a survey for stars with disks in the Taurus star-forming region usingthe Spitzer Space Telescope, we have discovered a pair of young brown dwarfs,FU Tau A and B, in the Barnard 215 dark cloud. They have a projected angularseparation of 5.7", corresponding to 800 AU at the distance of Taurus. Toassess the nature of these two objects, we have obtained spectra of them andhave constructed their spectral energy distributions. Both sources are young(~1 Myr) according to their Halpha emission, gravity-sensitive spectralfeatures, and mid-IR excess emission. The proper motion of FU Tau A providesadditional evidence of its membership in Taurus. We measure spectral types ofM7.25 and M9.25 for FU Tau A and B, respectively, which correspond to masses of~0.05 and ~0.015 M\cdot according to the evolutionary models of Chabrier andBaraffe. FU Tau A is significantly overluminous relative to an isochronepassing through FU Tau B and relative to other members of Taurus near itsspectral type, which may indicate that it is an unresolved binary. FU Tau A andB are likely to be components of a binary system based on the low probability(~3x10^-4) that Taurus would produce two unrelated brown dwarfs with aprojected separation of a