Preheat the oven to 450 degrees . In a large skillet, heat the olive oil over medium-high heat. Season the chicken with salt and pepper, add to the pan and cook, turning once, until cooked through, about 5 minutes. Let cool, then shred the meat.
Whisk together the salsa verde and ricotta; season with salt and pepper. In a greased 9-inch square baking dish, layer one-third of the salsa mixture, tortillas, chicken, onion, spinach and pepper jack; repeat twice. Bake until golden-brown, 15 to 20 minutes. Let stand for 10 minutes before serving.