Chalcones are natural compounds that are largely distributed in plants, fruits, and vegetables. They belong to the flavonoid group of molecules, and some of them exhibit numerous biological activities. The results of quantum chemical calculations (based on density functional theory, using the B3P86 exchange-correlation potential) are reported for 11 chalcones, in the gas phase and in the presence of an implicit solvent (using the conductor-like polarizable continuum model, C-PCM). These results are discussed in regard to the capacity of these chalcones to scavenge the 2,2-diphenyl-1-pycril-hydrazyl (DPPH) free radical. The O-H bond dissociation enthalpy (BDE) parameter, which is calculated for each OH group, seems to be the best indicator of the anti-radical property of these compounds. This demonstrates the importance of the H atom transfer mechanism to explain their capacity to scavenge the free radicals. The active sites are identified as the 6'-OH group and the 3,4-dihydroxy-catechol. The alpha,beta-double bond is influential in determining the activity.