Step 1Combine tomatillos, lime juice, Anaheim and serrano peppers, salt and cilantro in small serving bowl. Set aside.
Step 2Heat heavy 12-inch skillet over medium heat. Place tortilla in pan and sprinkle one-third of cheese and one-third of chicken evenly on top. Cover with second tortilla. When bottom tortilla is nicely browned, 2 to 2 1/2 minutes, use wide spatula to turn quesadilla. Brown other side. Place on cutting board. Repeat to cook other 2 quesadillas.
Step 3Use sharp knife or pizza cutter to cut each quesadilla into 6 wedges. Arrange wedges on warm platter and serve immediately. Pass salsa.