For the infusion: Combine the water and bleach in a large container. Dunk the tarragon and chives in the solution, and then rinse with cold water and pat dry. Place the herbs in a 2-quart container large enough to hold the vinegar.
Heat the vinegar in an electric kettle. When the vinegar reaches 190ºF, pour the vinegar over the herbs. After the vinegar has cooled, place the lid on the container, and store in a cool, dark place for 2 weeks.
For storage: After 2 weeks, sterilize the containers and lids that you will store the vinegar in by immersing them in a large pot of boiling water and boiling for 10 minutes. If using corks, purchase pre-sterilized corks, and then dip them in and out of boiling water 3 to 4 times.
Sanitize the second batch of herbs in the water and bleach solution, rinse, pat dry, and set aside. Divide the fresh herbs among the containers.
Strain the vinegar through a sanitized funnel lined with cheesecloth. Seal and refrigerate over the fresh herbs in the sanitized containers. Discard the old herbs. The vinegar may be stored at room temperature for 5 to 6 weeks, or in the refrigerator for up to 6 months.