Li(Ni 0.5 Mn 0.5 )O 2 is an exciting new Li-intercalation material for which high reversible capacity in rechargeable lithium batteries has been demonstrated, but whose structure has not been completely determined. We propose a structural arrangement in which cation layers with composition Li 11/12 Ni 1/12 alternate with Li 1/12 Ni 5/12 Mn 6/12 in the octahedral sites of the close-packed oxygen framework. In the layer with composition Li 1/12 Ni 5/12 Mn 6/12 the ions arrange in flower-like patterns, with Li surrounded by a hexagon of Mn, which in turn is surrounded by a larger hexagon of Ni. This ordering is consistent with available experimental information, and first-principles computations indicate that it is degenerate in energy with previously proposed structures. The intercalation potential and Li-site occupancies are calculated within this structure as a function of Li content by combining a cluster expansion with Monte Carlo simulations. Early in the charge cycle, the Li ions that are part of the flower ordering in the transition metal layer are removed, freeing up tetrahedral sites which then become occupied by lithium. Our results indicate that the tetrahedral Li require a high potential to be removed and effectively lower the attainable capacity of the material in practical voltage intervals.