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Sprinkle chicken with salt and pepper.
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Melt butter in heavy large skillet over medium-high heat.
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Add chicken and cook until brown on both sides, about 5 minutes.
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Transfer chicken to plate.
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Add green and red bell peppers and onion to same skillet and saute until crisp-tender, about 5 minutes.
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Add minced garlic and crushed red pepper to skillet and saute 4 minutes.
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Add whipping cream and chicken stock.
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Simmer until sauce thickens slightly, about 8 minutes.
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Cut chicken into strips and add to sauce.
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Simmer until chicken is cooked through, about 2 minutes.
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Add basil and 1/4 cup grated Parmesan cheese to sauce, stirring to incorporate.
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Season sauce to taste with salt and pepper.
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Meanwhile, cook pasta in large pot of boiling salted water until tender but still firm to bite.
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Drain and return to pot.
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Add sauce and toss to coat.
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Serve, passing additional Parmesan separately.
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Makes 4 first-course servings.