The LHC will have unprecedented sensitivity to flavor-changing neutral current (FCNC) top quark decays, whose observation would be a clear sign of physics beyond the standard model. Although many details of top flavor violation are model dependent, the standard model gauge symmetries relate top FCNCs to other processes, which are strongly constrained by existing data. We study these constraints in a model independent way, using a low energy effective theory from which the new physics is integrated out. We consider the most important operators which contribute to top FCNCs and analyze the current constraints on them. We find that the data rule out top FCNCs at a level observable at the LHC due to most of the operators comprising left-handed first or second generation quark fields, while there remains a substantial window for top decays mediated by operators with right-handed charm or up quarks. If FCNC top decays are observed at the LHC, such an analysis may help decipher the underlying physics.