Combine the sugar, water, and corn syrup in medium saucepan and cook over medium-high heat for about 10 minutes, until all the sugar is dissolved. Do not allow the syrup to come to a full rolling boil.
While the sugar is cooking, finely chop the basil and place half in a mesh bag or loose-tea steeper and add to the sugar mixture. Set the other half aside.
When slightly cooled, remove cooked basil, add fresh basil and chill.