Combine rice-vermicelli mix and butter in a large saucepan over medium heat. Cook and stir until vermicelli is golden brown. Slowly stir in water and seasoning packet; bring to a boil. Cover, reduce heat to medium-low, and simmer until rice is tender, 20 to 25 minutes. Remove from heat and let sit, covered, for 3 to 5 minutes. Transfer rice to a large serving bowl and place in the refrigerator to chill.

Add green onions, water chestnuts, celery, chicken, mayonnaise, Worcestershire sauce, salt, and pepper to rice in the bowl; mix until well combined. Chill in the refrigerator until serving time.