We report the discovery of a binary composed of two brown dwarfs, based on the analysis of the microlensing event OGLE-2016-BLG-1469. Thanks to detection of both finite-source and microlens-parallax effects, we are able to measure both the masses $M_1sim 0.05 M_odot$, $M_2sim 0.01 M_odot$, and distance $D_{rm L} sim 4.5$ kpc, as well as the projected separation $a_perp sim 0.33$ au. This is the third brown-dwarf binary detected using the microlensing method, demonstrating the usefulness of microlensing in detecting field brown-dwarf binaries with separations less than 1 au.