  We identify Gaia0007-1605AC as the first inner brown dwarf-white dwarf binary
of a hierarchical triple system in which the outer component is another white
dwarf (Gaia0007-1605B). From optical/near-infrared spectroscopy obtained at the
Very Large Telescope with the X-Shooter instrument and/or from Gaia photometry
plus SED fitting, we determine the effective temperatures and masses of the two
white dwarfs (12018+-68 K, 0.54+-0.01 Msun for Gaia0007-1605A and 4445+-116 K,
0.56+-0.05 Msun for Gaia0007-1605B) and the effective temperature of the brown
dwarf (1850+-50 K; corresponding to a spectral type L3+-1). By analysing the
available TESS light curves of Gaia0007-1605AC we detect a signal at
1.0446+-0.0015 days with an amplitude of 6.25 ppt, which we interpret as the
orbital period modulated from irradiation effects of the white dwarf on the
brown dwarf's surface. This drives us to speculate that the inner binary
evolved through a common envelope phase in the past. Using the outer white
dwarf as a cosmochronometer and analysing the kinematic properties of the
system, we conclude that the triple system is about 10 Gyr old.
