Tip:Variation: Use small gratin dishes to make individual servings.
Heat a gas grill to medium high or build a medium-hot charcoal fire. Coat the chicken with olive oil and season generously with salt and pepper. Grill the chicken breasts until just cooked through, 4 to 5 min. per side. When cool enough to handle, slice into thin strips. Heat the oven to 450°F.
In a small skillet, heat the 3 tablespoons oil over medium-high heat until very hot (dip the edge of a tortilla in to check; it should sizzle straight away). Using tongs, set a tortilla in the hot oil and cook until soft and lightly brown on each side, 15 to 20 seconds per side. Transfer to paper towels to cool and drain. If the pan gets dry, add another tablespoon of oil.
In a baking dish large enough to accommodate four separate stacks of tortillas (a 10x15-inch Pyrex dish is good), ladle a thin layer of sauce. Lay four tortillas in the dish and ladle about 1/2 cup of sauce over them. Divide half the chicken among the first layer of tortillas and top with another 1/2 cup of sauce and a third of the cheese. Stack on another four tortillas, and top with the rest of the chicken, then more sauce and another third of the cheese. Finish with a third tortilla layer, and top with the remaining sauce and cheese. Bake until the sauce has thickened somewhat, about 20 min. The edges of the top tortilla in each stack will turn golden, but if they look like they’re drying out too much or burning, occasionally spoon some sauce over them. Let rest for 5 to 10 min. before serving. To serve, transfer each stack with a spatula to a dinner plate. Spoon any sauce left in the baking dish over the stacks and sprinkle with chopped cilantro if you like.