The correct prediction of the abundances of the light nuclides produced during the epoch of Big Bang Nucleosynthesis (BBN) is one of the main topics of modern cosmology. For many of the nuclear re- actions that are relevant for this epoch, direct experimental cross section data are available, ushering the so-called “age of precision”. The present work addresses an exception to this current status: the 2 H( α, γ) 6 Li reaction that controls 6 Li production in the Big Bang. Recent controversial observations of 6 Li in metal-poor stars have heightened the interest in understanding primordial 6 Li production. If confirmed, these observations would lead to a second cosmological lithium problem, in addition to the well-known 7 Li problem. In the present work, the direct experimental cross section data on 2 H( α, γ) 6 Li in the BBN energy range are reported. The measurement has been performed deep underground at the LUNA (Lab- oratory for Underground Nuclear Astrophysics) 400 kV accelerator in the Laboratori Nazionali del Gran Sasso, Italy. The cross section has been directly measured at the energies of interest for Big Bang Nucle- osynthesis for the first time, at E cm = 80, 93, 120, and 133 keV. Based on the new data, the 2 H( α, γ) 6 Li thermonuclear reaction rate has been derived. Our rate is even lower than previously reported, thus in- creasing the discrepancy between predicted Big Bang 6 Li abundance and the amount of primordial 6 Li inferred from observations.