Combine the sugar, water, and corn syrup in medium saucepan and cook over medium-high heat for about 12 minutes, until all sugar is completely 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 place into the sugar mixture. Set the other half aside.
When slightly cooled, remove cooked basil and add fresh basil to the syrup and chill in a storage container or squeeze bottle until ready to use. This will keep up to 2 months in the refrigerator or 6 months in the freezer.