Chop Tarragon. Heat vinegar in pan over low heat until hot. Do not let simmer.
Place tarragon and lemon in bowl. Stir in hot vinegar. Set aside to cool.
Cover tightly and refrigerate for 2-4 weeks. Gently stir every few days to blend flavors.
Strain vinegar through fine mesh then through a coffee filter. Funnel into bottles and cover tightly. Store at room temperature for up to 2 months.