We present multiepoch imaging of the T5.0+T5.5 binary 2MASS J15344984–2952274AB obtained with the Keck laser guide star adaptive optics system. Combined with archival HST imaging, our total data span ~50% of the orbital period. We use a Markov chain Monte Carlo analysis to determine a period of 15.1^{+ 2.3}_−1.6 yr and a total mass of 0.056 ± 0.003 M (59 ± 3 M_J). This is the first field binary for which both components are confirmed to be substellar. This is also the coolest and lowest mass binary with a dynamical mass to date. Using evolutionary models and accounting for the measurement covariances, we derive an age of 0.78 ± 0.09 Gyr and a mass ratio of 0.936^{+ 0.012}_−0.008. The relatively youthful age is consistent with the low tangential velocity of this system. For the individual components, we find T_eff = 1028 ± 17 and 978 ± 17 K and masses of 0.0287 ± 0.0016 M (30.1 ± 1.7 M_J) and 0.0269 ± 0.0016 M (28.2 ± 1.7 M_J). These values generally agree with previous studies of T dwarfs and affirm current theoretical models. However, (1) the temperatures are about 100 K cooler than derived for similar objects and suggest that the representative ages of field brown dwarfs may be overestimated. Similarly, (2) the H-R diagram positions are discrepant with current models and taken at face value would overestimate the masses. While this may arise from errors in the luminosities and/or radii predicted by evolutionary models, the likely cause is a modest (100 K) overestimate in temperature determined from model atmospheres. We elucidate future tests of theory as the sample of dynamical masses grows. In particular, we suggest that low-mass field binaries with dynamical masses ("mass benchmarks") can serve as reference points for T_eff and log g to constrain atmospheric models, as good as or even better than single brown dwarfs with age estimates ("age benchmarks").