Drain the pasta, reserving 1/4 cup of the cooking liquid. Place radicchio and the reserved liquid in the pot and cook over medium heat, stirring constantly, until wilted, 2 to 3 minutes. Stir in the pasta, 2 tablespoons Parmesan, oil, chicken, vinegar and pepper and continue cooking until the cheese starts to melt, 1 to 2 minutes. Serve the pasta garnished with walnuts and the remaining cheese.
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