Place the chicken breasts in pot along with 1⁄2 an onion, salt and cover with water. Bring to a boil and simmer until cooked through, about 20 minutes.
Remove chicken from the water and let cool slightly. Shred chicken with two forks and set aside.
Dice the remaining onion and add to the shredded chicken.
Individually warm 6 tortillas on the stove to make them pliable so they don't crack. Keep them covered with a dish cloth to stay warm, then working one by one dip each warm tortilla in salsa verde. Scoop two heaping tablespoons into each tortilla, roll tightly and place in a large casserole dish, seam side down, in a single layer. Repeat with the remaining tortillas and chicken.
Drench entire pan with 1 cup sauce and sprinkle with crumbled queso fresco.
Bake, covered in oven for 25 to 30 minutes. Remove from oven and serve with sour cream, shredded lettuce and additional queso fresco, if desired.