(Abridged) We present Keck, HST, and Gemini-North observations of the L4+L4 binary HD 130948BC which together span ~70% of the binarys orbital period. We determine a total dynamical mass of 0.109+/-0.002 Msun (114+/-2 Mjup). The flux ratio is near unity, so both components are unambiguously substellar for any plausible mass ratio. An independent constraint on the age of the system is available from the G2V primary HD 130948A. The available indicators suggest an age comparable to the Hyades, with the most precise age being 0.79 Gyr based on gyrochronology. Therefore, HD 130948BC is now a unique benchmark among field L and T dwarfs, with a well-determined mass, luminosity, and age. We find that substellar theoretical models disagree with our observations. Both components of HD 130948BC appear to be overluminous by a factor of ~2-3x compared to evolutionary models. The age of the system would have to be notably younger than the gyro age to ameliorate the luminosity disagreement. However, regardless of the adopted age, evolutionary and atmospheric models give inconsistent results, indicating systematic errors in at least one class of models, possibly both. The masses of HD 130948BC happen to be very near the theoretical mass limit for lithium burning, and thus measuring the differential lithium depletion between B and C will provide a uniquely discriminating test of theoretical models. The potential underestimate of luminosities by evolutionary models would have wide-ranging implications; therefore, a more refined age estimate for HD 130948A is critically needed.
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