Sterilize the glass bottles or jars that will hold the tarragon vinegar. Process them in boiling water or in the hot cycle in an automatic dishwasher.
Rinse the tarragon thoroughly in cool water. Allow to drain on paper towels.
Place half the tarragon (two sprigs each) into the sterilized bottles.
In a 2.5-qt. sauce pan, heat the vinegar over medium heat until it reaches 190°F/88°C.
Pour the hot vinegar into the bottles with the tarragon and cap tightly. Let the mixture sit for two to three weeks in a cool, dark place.
Date bottle and strain the tarragon stalks from the vinegar and discard before using.