The binary nature of the M8.5 dwarf DENIS J063001.4-184014AB (DE0630-18) was discovered with astrometric monitoring from the ground, which determined the unresolved photocentric orbit and the trigonometric parallax of the system. Here we present radial velocity monitoring and resolved observations in the near-infrared with Keck aperture masking that allows us to measure the system's relative separation and brightness. By combining all available information, we determine the individual dynamical masses of the binary components to be $M_1 = 0.052^{+0.009}_{-0.008}$ MSun and $M_2 = 0.052^{+0.005}_{-0.004}$ MSun, both firmly in the substellar regime. These masses are surprising, given the object's M8.5 optical spectral type and equivalent absolute magnitude, and the significant difference in brightness between the components (∆K = 1.74 ± 0.06 mag). Our results suggest that DE0630-18 is a relatively young system (∼200 Myr) with a secondary component that is itself a potentially unresolved binary.