Reserve 1 teaspoon taco seasoning mix; set aside. Combine remaining taco seasoning mix, chicken, beer, and chiles in a large skillet; bring to a boil. Reduce heat, and simmer, uncovered, 5 minutes or until mixture is thickened. Remove from heat; stir in salsa.
Mash beans and garlic until smooth; stir in cilantro. Spread bean mixture in a 10-inch quiche dish. Spoon chicken mixture evenly over bean mixture; top with cheese. Bake, uncovered, at 375° for 15 minutes or until cheese melts and mixture is thoroughly heated.
Combine sour cream and reserved 1 teaspoon taco seasoning mix; spread over melted cheese. Top with tomato, green onions, and olives. Serve with no-oil baked tortilla chips.