Combining experimental spectroscopy and hybrid density functional theory calculations, we show that the incorporation of fluoride ions into a prototypical reducible oxide surface, namely, ceria(111), can induce a variety of nontrivial changes to the local electronic structure, beyond the expected increase in the number of Ce ions. Our resonant photoemission spectroscopy results reveal new states above, within, and below the valence band, which are unique to the presence of fluoride ions at the surface. With the help of hybrid density functional calculations, we show that the different states arise from fluoride ions in different atomic layers in the near surface region. In particular, we identify a structure in which a fluoride ion substitutes for an oxygen ion at the surface, with a second fluoride ion on top of a surface Ce ion giving rise to F 2p states which overlap the top of the O 2p band. The nature of this adsorbate F-Ce resonant enhancement feature suggests that this bond is at least partially covalent. Our results demonstrate the versatility of anion doping as a potential means of tuning the valence band electronic structure of ceria.