Heat half of the oil in a non-stick pan over medium heat. Sauté the onion and garlic for 3-4 minutes. Add the spinach and cook until it is wilted. Season with salt and pepper. Remove from the heat and drain as much of the moisture out of the spinach as you can.
Season the diced chicken well with salt and pepper. Mix in the spinach, feta, and eggs.
Drape the phyllo sheets into a lightly greased (with non-stick spray) round baking dish, springform pan or round oven-safe vessel so they are overlapping. Place the chicken spinach mixture into the center and fold the phyllo sheets over the top. Tuck everything in so it's somewhat tight. Brush the outside with the remaining oil.
Bake in the oven until golden brown and crispy and the internal temperature reaches 165°F using a thermometer, approximately 30 minutes.