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1.
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Browning the chicken.
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Season both sides of the chicken breasts with salt and pepper.
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Heat the oil in a large (10 to 12-inch) skillet over medium-high heat.
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Using tongs, carefully lower the chicken breasts into the pan and cook them for about 1 minute on each side just untilt hey begin to brown slightly.
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Transfer the still-raw chicken to a plate.
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2.
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Poaching in cream.
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Reduce the heat under the skillet to low.
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Add the shallot and cook, stirring constantly, until softened but not browned, less than 1 minute.
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Add the vermouth and cook for 30 seconds, then add the cream and half the tarragon.
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Return the chicken breasts to the pan and adjust the heat so that the cream gently simmers.
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Cover and cook until the chicken is firm and just cooked through, 4 to 6 minutes.
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To check for doneness, cut into the thickest part of a breast with a pairing knife there should be no sign of pink or translucence.
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15
3.
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Finishing.
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Transfer the chicken breasts to a warmed serving platter or individual dinner plates.
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The sauce should be thick enough to lightly coat a spoon.
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If it is too thin, continue to simmer it for about 1 minute and it will thicken.
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Stir in the remaining tarragon and the lemon juice, then taste and season with additional salt and pepper if needed.
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Pour the sauce over the chicken and serve right away with buttered egg noodles.
