Place wine and vinegar in a saucepan over low heat. Bring to scalding but do not boil.
Meanwhile, wash basil and place in a sterilized quart jar. Pour hot liquid slowly over basil. Seal tightly and store in a dark place for 3 weeks.
Strain vinegar through cheesecloth and pour into smaller sterilized bottles. Add a sprig of basil to each bottle, if you wish.
Makes 1 quart.