A method is proposed for the preparation of stable sols of nanocrystalline cerium dioxide in nonpolar solvents, based on surface modification of CeO2 nanoparticles obtained by thermal hydrolysis of concentrated aqueous solutions of ammonium cerium(IV) nitrate with residues of 2-ethylhexanoic and octanoic acids. The synthesis was carried out at temperatures below 100 °C and did not require the use of expensive and toxic reagents. An assessment of the radical-scavenging properties of the obtained sols using the superoxide anion-radical neutralization model revealed that they demonstrate notable antioxidant activity. The results obtained indicate the potential of the nanoscale cerium dioxide sols in nonpolar solvents to be used for creating nanobiomaterials possessing antioxidant properties.