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Place the walnuts in a food processor and run until ground. Set aside.
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Melt the butter in a medium saucepan. Add the onion and garlic.
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Cook until soft (Do Not Brown). Add the broth, herbs, and walnuts. Bring to a boil.
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Reduce the heat and simmer until slightly thickened.
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Grill the chicken while the sauce reduces.
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Serve the chicken with the warm sauce ladled on top.