Preheat the oven to 350°F (175°C). If using a broiler, arrange an oven-safe dish for later broiling.
In a mixing bowl, combine the softened cream cheese, sour cream, and salsa verde until smooth and evenly mixed.
Stir in the shredded chicken, 3/4 cup of the shredded cheese, and lime juice if using; season with salt and pepper to taste.
Spoon the mixture into a baking dish and spread evenly.
Bake for 15–20 minutes until heated through and bubbly; if you want a browned top, sprinkle remaining cheese and broil 1–2 minutes until golden.
Remove from oven and let rest 2–3 minutes before serving with chips, crackers, or vegetables.