Preheat the oven to 425°. On a baking sheet, toss the chicken with 1 tablespoon oil and season with salt and pepper. Bake until browned and cooked through, about 40 minutes.
Meanwhile, in a saucepan, combine the tomatillos and just enough water to cover. Bring to a boil, then simmer until tender,a bout 5 minutes. using a slotted spoon, transfer the tomatillos to a food processor; reserve 1/3 cup cooking water. Puree the tomatillos with the onion, jalapeño, garlic and sugar.
In a skillet, heat the remaining 2 tablespoons oil over medium-high heat. Add the tomatillo puree and cook, stirring, for 10 minutes. Stir in the reserved cooking water and 1 tablespoon cilantro. Top the tortilla strips with the chicken, sauce and remaining 1 tablespoon cilantro.