Recent observations of 6Li in metal poor stars suggest a large production of this isotope during big bang nucleosynthesis (BBN). In standard BBN calculations, the 2H(α,γ)6Li reaction dominates 6Li production.This reaction has never been measured inside the BBN energy region because its cross section drops exponentially at low energy and because the electric dipole transition is strongly suppressed for the isoscalar particles 2H and α at energies below the Coulomb barrier. Indirect measurements using the Coulomb dissociation of 6Li only give upper limits owing to the dominance of nuclear breakup processes.Here, we report on the results of the first measurement of the 2H(α,γ)6Li cross section at big bang energies. The experiment was performed deep underground at the LUNA 400 kV accelerator in Gran Sasso, Italy.The primordial 6Li/7Li isotopic abundance ratio has been determined to be (1.5 +- 0.3) × 10−5, from ourexperimental data and standard BBN theory. The much higher 6Li=7Li values reported for halo stars willlikely require a nonstandard physics explanation, as discussed in the literature.