In this letter we present preliminary results of full six dimensional quantum dynamics calculations for dissociative adsorption of a hydrogen molecule on a Cu(111) surface. We utilize the time-dependent wave-packet approach to simulate the dissociation process on a full dimensional LEPS potential energy surface which has incorporated the latest ab initio data [Hammer et al. Phys. Rev. Lett. 73, 1400 (1994)]. We use a novel partitioning of the angular momentum operator In the split-operator method so that a direct product DVR can be rigorously implemented. The most interesting, observation in the present rigorous quantum dynamics study is the site-averaged effect, i.e., the averaged dissociation probability of the four dimensional calculations over the three symmetric impact sites strongly resembles the exact dissociation probability of the six dimensional calculations. In accord with the low dimensional calculations, initial vibrational excitation of H-2 effectively reduces the translational threshold energy. The rotational orientation effect observed in the four dimensional studies remains in the present full dimensional dynamics with the cartwheel orientation yielding dramatically lower dissociative efficiency than the energetically equivalent helicopter orientation. We focus on normal incident scattering. The diffractive scattering and more detailed results will be presented in a later paper.