Heat a large skillet over medium-high heat and stir in the ground turkey. Cook and stir until the turkey is crumbly, evenly browned, and no longer pink. Drain and discard any excess grease. Add bell pepper, onion, and celery. Continue to cook and stir until vegetables are tender, 5 to 10 minutes.
Stir chili beans, tomatoes, tomato sauce, beer, 1 chopped chipotle chile, cumin, and black pepper into turkey mixture; simmer for 2 hours.
Place Greek yogurt, mayonnaise, lime juice, garlic, and remaining 1 chopped chipotle chile in a food processor or blender; pulse until mixture is smooth. Refrigerate sauce until ready to use.
Scoop chili into bowls; sprinkle with Cheddar cheese and drizzle with yogurt sauce.