Soft X-ray spectromicroscopy at the O K-edge, U N4,5-edges and Ce M4,5-edges has been performed on focused ion beam sections of spent nuclear fuel for the first time, yielding chemical information on the sub-micrometer scale. To analyze these data, a modification to non-negative matrix factorization (NMF) was developed, in which the data are no longer required to be non-negative, but the non-negativity of the spectral components and fit coefficients is largely preserved. The modified NMF method was utilized at the O K-edge to distinguish between two components, one present in the bulk of the sample similar to UO2 and one present at the interface of the sample which is a hyperstoichiometric UO2+x species. The species maps are consistent with a model of a thin layer of UO2+x over the entire sample, which is likely explained by oxidation after focused ion beam (FIB) sectioning. In addition to the uranium oxide bulk of the sample, Ce measurements were also performed to investigate the oxidation state of that fission product, which is the subject of considerable interest. Analysis of the Ce spectra shows that Ce is in a predominantly trivalent state, with a possible contribution from tetravalent Ce. Atom probe analysis was performed to provide confirmation of the presence and localization of Ce in the spent fuel.