Fresh chives are a good source of antioxidants, but only if you're eating them in abundance. Why? Because with an ORAC value of around 2,000 you could could a similar amount from red leaf lettuce or kale. The difference is that you can easily eat 100 grams of those two leafy greens, doing so with raw fresh chives is unlikely. If you're only sprinkling a few chives on top of a soup or entree, don't count on getting much antioxidant content from them since it would only be a few grams of chives (remember the ORAC is for 100 grams worth).
USDA Database for the Oxygen Radical Absorbance Capacity (ORAC) of Selected Foods, Release 2 - Prepared by Nutrient Data Laboratory, Beltsville Human Nutrition Research Center (BHNRC), Agricultural Research Service (ARS), U.S. Department of Agriculture (USDA) - May 2010