Oxygen vacancies are an important type of defect in transition metal oxides. In SrTiO3 they are believed to be the main donors in an otherwise intrinsic crystal. At the same time, a relatively deep gap state associated with the vacancy is widely reported. To explain this inconsistency we investigate the effect of electron correlation in an oxygen vacancy (OV) in SrTiO3. When taking correlation into account, we find that the OV-induced localized level can at most trap one electron, while the second electron occupies the conduction band. Our results offer a natural explanation of how the OV in SrTiO3 can produce a deep in-gap level (about 1 eV below the conduction band bottom) in photoemission, and at the same time be an electron donor. Our analysis implies an OV in SrTiO3 should be fundamentally regarded as a magnetic impurity, whose deep level is always partially occupied due to the strong Coulomb repulsion. An OV-based Anderson impurity model is derived, and its implications are discussed. [14,20]. The OV in SrTiO 3 is particularly intriguing. On the one hand, the OV concentration is roughly proportional to that of the carriers [14,20,21], strongly suggesting that vacancies are electron donors; on the other hand, an OV produces an in-gap signal, peaked approximately 1.0 eV below the conduction band, in angle resolved photoemission spectroscopy (ARPES), even at temperatures as low as 20 K [14,19,22]. Within the single-particle description, the ARPES spectrum implies that an OV results in a deep impurity level and therefore is not likely to be the electron donor. In this Letter, we demonstrate that, by taking the correlation effect, these two seemingly conflicting observations can be naturally reconciled. More fundamentally, our analysis suggests that an OV in SrTiO 3 should be regarded as a magnetic impurity, in the sense that a deep level is always partially occupied due to the strong Coulomb repulsion, and may account for the observed Kondo physics [10] or interface ferromagnetismThe electronic structure of an OV in SrTiO 3 has been extensively studied using density functional theory (DFT) [23][24][25][26][27][28][29][30]. Depending on the functional used, the OV induced impurity level in SrTiO 3 can lie above the conduction band edge, thus leading to a resonance [26,28,29]; be an in-gap bound state with energy level position ranging from 0.4 to 1 eV below the conduction band bottom [25,28,30]; or be a partially filled, spin-polarized gap state [27].Independent of the functional, the OV-induced state is spatially localized and is mainly composed of the next-to-OV Ti 3d 3z 2 −r 2 and 4p z orbitals [31]. To include the correlation effect in an OV, we first identify the main change in the local electronic structure that it causes. The following discussion is based on Ref. [31]. Under cubic symmetry, the proper local orbital basis of a Ti atom consists of two 3d x 2 −y 2 , 3d 3z 2 −r 2 orbitals with e g symmetry, and three 3d