We present results for the electronic structure of α uranium using a recently developed quasiparticle self-consistent GW method (QSGW ). This is the first time that the f -orbital electron-electron interactions in an actinide has been treated by a first-principles method beyond the level of the generalized gradient approximation (GGA) to the local density approximation (LDA). We show that the QSGW approximation predicts an f -level shift upwards of about 0.5 eV with respect to the other metallic s-d states and that there is a significant f -band narrowing when compared to LDA band-structure results. Nonetheless, because of the overall low f -electron occupation number in uranium, ground-state properties and the occupied band structure around the Fermi energy is not significantly affected. The correlations predominate in the unoccupied part of the f states. This provides the first formal justification for the success of LDA and GGA calculations in describing the ground-state properties of this material. It has long been recognized that 5f electron-electron correlations play an important role in the light actinides [1,2], becoming increasingly significant as one moves across this series and the atomic number Z increases. This culminates in Pu, which has many extreme physical properties that are driven by these correlations [3], such as the large volume expansion for the α to δ phase transformation [4,5]. What is less clear is the role of correlations for Z's less than Pu. Uranium stands at a kind of threshold in this regard. Experimentally, the pure material is weak to moderately correlated [6], since specific heat enhancements are moderate and no convincing satellite or Kondo photoemission peaks are observed, which is consistent with the success of band-structure in predicting materials properties [7,8]. At the same time, when the uranium atoms are pushed apart by other elements, they form many heavy fermion and other strongly correlated uranium compounds [9]. In this regard, uranium is an inviting target to study, since it should have interesting correlation effects beyond conventional metals like copper or aluminum, and yet these should be weak enough to have some hope of accurately calculating them. It is thus an important testing ground for correlation theory and how many-body effects correct conventional LDA band structures.The most widely used electronic-structure method, the local density approximation (LDA), has been an immensely successful tool that reasonably predicts groundstate properties of weakly correlated systems. The LDA is much less successful at predicting optical properties of such systems, and its failures become more serious as correlations become stronger. Recent photoemission spectroscopy on high quality uranium singe crystals has revealed additional information about the electronic structure of this material [10,11]. Comparison with LDA calculated electronic bands shows some disagreement between experiment and theory. Because of the poor treatment of electron correlations by LDA it is dif...