Recent observations of (6)Li in metal poor stars suggest a large production of this isotope during big bang nucleosynthesis (BBN). In standard BBN calculations, the (2)H(α,γ)(6)Li reaction dominates (6)Li 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 (2)H and α at energies below the Coulomb barrier. Indirect measurements using the Coulomb dissociation of (6)Li only give upper limits owing to the dominance of nuclear breakup processes. Here, we report on the results of the first measurement of the (2)H(α,γ)(6)Li cross section at big bang energies. The experiment was performed deep underground at the LUNA 400 kV accelerator in Gran Sasso, Italy. The primordial (6)Li/(7)Li isotopic abundance ratio has been determined to be (1.5 ± 0.3) × 10(-5), from our experimental data and standard BBN theory. The much higher (6)Li/(7)Li values reported for halo stars will likely require a nonstandard physics explanation, as discussed in the literature.