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1
Preheat the oven to 400 degrees F.
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2
Put the garlic halves, cut side down, on a sheet of aluminum foil on a rimmed baking sheet.
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3
Add 2 tablespoons chicken stock and wrap the foil around the garlic, keeping the cut sides flat on the sheet tray.
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4
Roast until the garlic is very soft, about 30 minutes.
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5
Remove the garlic from the oven and let stand until cool enough to handle.
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6
Squeeze the soft garlic from the head with your fingers into a large saucepan.
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7
Whisk in 1 cup of the stock to loosen the garlic paste and put the pot over medium-high heat.
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8
Add the remaining stock, lemon juice, and chopped tarragon; season with salt and pepper, to taste.
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9
Bring the mixture to a boil, then reduce the heat to a simmer and add the chicken.
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10
Cover and cook until the chicken is just cooked through, about 9 to 12 minutes.
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11
Ladle the soup into bowls and garnish with thin slices of lemon and a sprinkle of fresh tarragon leaves.