A process for converting light paraffins to a high octane gasoline composition is disclosed. The process involves: (1) oxidation of iso-paraffins to alkyl hydroperoxides and alcohol; (2) conversion of the alkyl hydroperoxides and alcohol to dialkyl peroxides; and (3) radical coupling of iso-paraffins using the dialkyl peroxides as radical initiators, thereby forming gasoline-range molecules. Fractionation of the gasoline-range molecules can then be used to isolate high octane gasoline fractions having a road octane number [(RON+MON)/2] greater than 110.