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1
Place the chicken thighs in a 6-quart Dutch oven or soup pot.
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2
Peel the onion, cut it into 4 pieces, and add them to the pot.
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3
Cut the celery into 4 pieces and add them to the pot.
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4
Peel the carrot, cut it into roughly 1-inch pieces, and add them to the pot.
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5
Sprinkle the tarragon and black pepper over the chicken and vegetables.
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6
Add just enough cold water to cover the chicken and vegetables completely, then sprinkle in the salt, if using.
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7
Cover the pot and bring to a rolling boil over high heat.
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8
As soon as the water reaches a vigorous boil, reduce the heat to low and cook the chicken, uncovered, at a very slow boil for 10 minutes.
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9
Then remove the pot from the heat and let it stand, covered, until the chicken is no longer pink in the center, 25 to 35 minutes.
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10
(Test for doneness by removing a thigh and cutting into it.
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11
The exact time will depend on the size of the thighs.)
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12
When the chicken is done, remove it from the pot, using tongs or a slotted spoon.
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13
(Reserve the chicken stock in the pot for later use.)
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14
Allow the chicken to cool enough to remove the skin and any visible fat.
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15
Pull the meat from the bones.
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16
Cut the chicken into bite-size chunks for future use.
