We present submillimeter observations of the young brown dwarfs KPNO Tau 1, KPNO Tau 3, and KPNO Tau 6 at 450 micron and 850 micron taken with the Submillimeter Common-User Bolometer Array on the James Clerke Maxwell Telescope. KPNO Tau 3 and KPNO Tau 6 have been previously identified as Class II objects hosting accretion disks, whereas KPNO Tau 1 has been identified as a Class III object and shows no evidence of circumsubstellar material. Our 3 sigma detection of cold dust around KPNO Tau 3 implies a total disk mass of (4.0 +/- 1.1) x 10^{-4} Msolar (assuming a gas to dust ratio of 100:1). We place tight constraints on any disks around KPNO Tau 1 or KPNO Tau 6 of <2.1 x 10^{-4} Msolar and <2.7 x 10^{-4} Msolar, respectively. Modeling the spectral energy distribution of KPNO Tau 3 and its disk suggests the disk properties (geometry, dust mass, and grain size distribution) are consistent with observations of other brown dwarf disks and low-mass T-Tauri stars. In particular, the disk-to-host mass ratio for KPNO Tau 3 is congruent with the scenario that at least some brown dwarfs form via the same mechanism as low-mass stars.
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