We report the discovery of the youngest brown dwarf with a disk within ~100 pc of the Sun via the Disk Detective citizen science project. We establish that the brown dwarf is located in the 3.7+4.6-1.4 Myr old ε Cha moving group. Its SED exhibits clear evidence of an IR excess, indicative of the presence of a warm circumstellar disk. Modeling this warm disk, we find Teff,disk = 521 K and LIR/L* = 0.14. The near-IR spectrum of the object matches a spectral type of M6γ ± 0.5, which corresponds to a low surface gravity object, and lacks distinctive signatures of accretion. Both our SED fitting and spectral analysis indicate the source is cool (Teff = 2784-2850 K) and well within the brown dwarf mass regime (42-58 MJup). The source is the youngest (<10 Myr) brown dwarf with a disk known within ~100 pc, and its proximity makes the system an ideal benchmark system to investigate the formation and early evolution of brown dwarfs. We acknowledge support from grant 14-ADAP14-0161 from the NASA Astrophysics Data Analysis Program and grant 16-XRP16_2-0127 from the NASA Exoplanets Research Program.