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Use a wide, heavy pot that has a lid. Set the pot over medium-high heat and add the grapeseed oil.
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Season the chicken with salt and pepper on both sides.
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Sear the chicken, skin side down, for about 3 minutes or until golden brown and crispy. Flip the chicken over and repeat. Transfer to a plate and set aside.
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Reduce the heat to medium, and sauté the leeks until softened, 3 to 4 minutes.
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Add the mushrooms and cook until they are lightly caramelized. Stir in the garlic and cook an additional minute.
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Deglaze the pan with the vinegar and wine, and reduce the liquid by half of its original volume.
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Add the chicken thighs and chicken stock to the pan. Bring the stock to a boil, and then reduce to a simmer. Cover and cook until the thighs are tender, about 40 minutes.
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Stir in the heavy cream, artichokes and peas, and cook until just heated through.
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Add the tarragon, and season with salt and pepper to taste.
