Combine chicken stock, rice, and seasoning packet in a saucepan; stir well. Bring to a boil over high heat. Cover and reduce heat to medium-low. Simmer 20 minutes. Remove from heat; allow to cool about 20 minutes. Refrigerate until chilled through.
Place rice in a serving bowl. Stir in black beans, avocado, mango, chopped chipotle chile, and cilantro. Drizzle with lime juice and toss. If salad seems too dry, add an additional tablespoon lime juice.