Wash tarragon; dry. In stainless-steel saucepan combine tarragon and vinegar; bring to boiling. Remove; cover with cheesecloth; cool. Pour into clean 1-quart jar; submerge tarragon. Cover with nonmetallic lid or plastic wrap; seal with metal lid. Let stand in cool, dark place for 1 to 2 weeks.
Line colander with cheesecloth. Strain vinegar. Transfer to clean 1-1/2-pint jar. Cover with nonmetallic lid or plastic wrap; tightly seal with metal lid. Store in cool, dark place up to 6 months. Makes about 2 cups (32, 1 tablespoon servings).