Electron spin resonance of Eu2+ (4 f7, S=7 2) in a La hexaboride (La B6) single crystal shows a single anisotropic Dysonian resonance. From the observed negative g shift of the resonance, it is inferred that the Eu2+ ions are covalent exchange coupled to the B 2p -like host conduction electrons. From the anisotropy of the spectra (linewidth and field for resonance), we found that the S ground state of Eu2+ ions experience a cubic crystal field of a negative fourth order crystal field parameter (CFP), b4 =-11.5 (2.0) Oe, in agreement with the negative fourth order CFP, A4, found for the non- S ground state R hexaborides. These results support covalency as the dominant contribution to the fourth order CFP for the whole R hexaboride family. © 2007 The American Physical Society.