Experimental data for the reaction p(n,γ?)d are scarce at energies relevant to Big Bang nucleosynthesis. In network calculations, the reaction rate used relies on theoretical models constrained by nucleon-nucleon scattering data, the capture cross section for thermal neutrons and experimental data of the inverse reaction d(γ?,n)p. The latter reaction - the photodissociation of the deuteron - is also sparsely investigated at Big-Bang energies. A comparison of measurements with precise calculations is difficult due to large experimental uncertainties. To address the need for precise experimental data we started to measure the cross section of the reaction d(γ?,n)p. We use high-intensity bremsstrahlung with an endpoint energy of 5.0 MeV generated at the superconducting electron accelerator ELBE at Forschungszentrum Dresden- Rossendorf. The incoming photon flux is determined by photon scattering at 27Al by measuring the well known transitions at 2.2 and 3.0 MeV with high-purity germanium detectors. With a pulse length of a few ps and an adjustable repetition rate, ELBE offers ideal conditions for precise time-of-flight experiments. For neutron detection we use plastic scintillators read out on two sides by high-gain photomultipliers. With this setup we can measure neutrons between 20 keV and 1.4 MeV with an energy resolution of about 4 %. The statistical uncertainty reached so far is about 5 %, the analysis of systematic effects is ongoing.