In a large pot, melt 3 tablespoons of butter over medium heat. Add the Rice-A-Roni Chicken Flavor mix along with the vermicelli noodles, stirring frequently until the mixture turns golden brown, about 3-5 minutes.

Pour in 5 cups of water, stirring to combine. Bring to a rapid boil, then reduce heat to low, cover, and simmer for 20-25 minutes or until rice is tender and liquid is absorbed. Remove from heat and let sit, covered, for an additional 5 minutes.

Carefully transfer the cooked Rice-A-Roni to a large mixing bowl. Refrigerate until cooled completely, about 30 minutes.

Once the rice is cool, mix in chopped green onions, sliced water chestnuts, diced celery, and shredded cooked chicken. Stir in mayonnaise, Worcestershire sauce, salt, and pepper to taste.

Cover with plastic wrap and chill in the refrigerator for at least an hour before serving.