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1
Preheat the oven to 375 degrees F.
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2
Heat a medium-large skillet over high heat.
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3
Add the olive oil.
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4
Season the chicken all over with salt and pepper, and lay the pieces in the pan rounded-side down first (the side that had the skin).
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5
Cook the chicken, turning only once, until golden brown on both sides, about 5 minutes.
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6
Transfer chicken to an oven-proof dish, reserving the skillet.
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7
Place the chicken to the oven and bake until an instant-read thermometer inserted into the thickest part of the chicken registers 170 to 75 degrees F, about 15 minutes.
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8
Meanwhile, pour the vermouth into the reserved skillet, scraping up any browned bits that cling to the pan with a wooden spoon, and cook over medium heat until the liquid reduces by about half.
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9
Add the chicken broth and continue to cook until slightly thickened.
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10
In a small bowl whisk a teaspoon or so of cold water with the cornstarch, then whisk the mixture into the broth and bring to a full boil.
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11
Remove from heat and add the zest, lemon juice, and tarragon.
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12
Season with salt and pepper, to taste.
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13
Remove the chicken from the oven.
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14
Pour any pan drippings from the chicken into the sauce and stir to combine.
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15
Divide the chicken pieces between 4 plates.
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16
Pour the sauce over the chicken and serve.
