Combine onion and oil in a pot and sauté over medium-high heat, 4 to 7 minutes. Mix in cumin and oregano and cook 30 seconds. Stir in chilies, tomato paste, vinegar, and 1/2 cup water. Let boil, then lower heat, and simmer 5 minutes. Mix in chicken and heat until hot.
Lay tortilla chips in one layer on the bottom of a baking sheet. Top with cheese and chicken mixture.
Bake 3 minutes or until cheese melts. Using a spatula, move chips to a serving platter and top with Cilantro-Avocado Cream and cilantro.
To make the Cilantro-Avocado Cream: In a small bowl, combine 1/3 cup finely diced firm-ripe avocado, 2 tablespoons sour cream, 1 tablespoon finely chopped fresh cilantro leaves, 2 teaspoons lime juice, and 2 teaspoons milk. Sprinkle with salt to taste.