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We report the discovery of the youngest brown dwarf with a disk at 102 pc from the Sun, WISEA~J120037.79-784508.3 (W1200-7845), via the Disk Detective citizen science project. We establish that W1200-7845 is located in the 3.7$\substack{+4.6 \\ -1.4}$ Myr-old $\varepsilon$~Cha association. Its spectral energy distribution (SED) exhibits clear evidence of an infrared (IR) excess, indicative of the presence of a warm circumstellar disk. Modeling this warm disk, we find the data are best fit using a power-law description with a slope $\alpha = -0.94$, which suggests it is a young, Class II type disk. Using a single blackbody disk fit, we find $T_{eff, disk} = 521 K$ and $L_{IR}/L_{*} = 0.14$. The near-infrared spectrum of W1200-7845 matches a spectral type of M6.0$\gamma \pm 0.5$, which corresponds to a low surface gravity object, and lacks distinctive signatures of strong Pa$\beta$ or Br$\gamma$ accretion. Both our SED fitting and spectral analysis indicate the source is cool ($T_{eff} = $2784-2850 K), with a mass of 42-58 $M_{Jup}$, well within the brown dwarf regime. The proximity of this young brown dwarf disk makes the system an ideal benchmark for investigating the formation and early evolution of brown dwarfs.