We investigate the dissociation of H_{2}^{+} into a proton and a H^{0} after single ionization with photons of an energy close to the threshold. We find that the p^{+} and the H^{0} do not emerge symmetrically in the case of the H_{2}^{+} dissociating along the 1sσ_{g} ground state. Instead, a preference for the ejection of the p^{+} in the direction of the escaping photoelectron can be observed. This symmetry breaking is strongest for very small electron energies. Our experiment is consistent with a recent prediction by Serov and Kheifets [Phys. Rev. A 89, 031402 (2014)]. In their model, which treats the photoelectron classically, the symmetry breaking is induced by the retroaction of the long-range Coulomb potential onto the dissociating H_{2}^{+}.