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1
Bring a large pot of salted water to a boil, add linguine and cook until a little less than al dente, about 8 minutes.
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2
Season chicken breasts with salt and pepper.
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3
Heat a deep skillet over medium-high heat.
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4
Add oil and 1 tablespoon of butter, heat until the butter is melted.
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5
Then add the chicken breasts, skin side down and cook for 2 to 3 minutes on each side, or until lightly colored.
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6
When done, transfer chicken breasts to a plate and set aside.
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7
Discard any fat from your skillet.
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8
Now, to the skillet add 2 tablespoons of butter, heat until butter is melted.
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9
Add onion, celery, carrots and salt and pepper.
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10
Cook, stirring until vegetables are softened, about 3 minutes.
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11
Return chicken to the skillet, add rosemary, and bay leaf and cook, covered over moderately low heat for 5 minutes more or until chicken is cooked through but still slightly springy to the touch.
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12
Again, remove chicken from the skillet and transfer to a plate, pouring any remaining juice into the skillet and set aside.
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13
Now, prepare the sauce.
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14
To the same skillet add madeira and chicken broth, cook until reduced by half.
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15
Then add heavy cream and reduce until sauce is lightly thickened.
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16
Drain and pat dry linguine and transfer to a serving plate and toss with remaining tablespoon of butter.
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17
Top with chicken breasts.
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18
To the sauce add minced fresh herbs, taste for seasoning, adding salt, pepper and lemon juice to taste.
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19
Gently pour sauce over linguine and chicken, making sure to evenly coat the entire surface.
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20
Serve immediately.
