Place chicken in a large pot. Add onion, garlic, peppercorns, and enough water to cover. Cover pot, and bring to a boil. Simmer, uncovered, until cooked through, 50 to 60 minutes. Remove chicken from cooking liquid, and set aside until cool enough to handle. Remove skin, and discard. Shred 3 cups of chicken, and set aside. Reserve remaining chicken for another use.
Line a basket or a bowl with a clean kitchen towel. Place tortillas, one at a time, over medium heat directly on a gas burner. Cook until edges are beginning to blacken, about 30 seconds. Turn, and cook until edges of second side begin to blacken, about 20 seconds more. Turn once more, and cook until tortilla puffs slightly, about 10 seconds more. Transfer to towel-lined basket, and enclose in towel. Repeat with remaining tortillas, adding each to the basket when done. If making ahead, wrap in aluminum foil, and reheat in a 350-degree oven.
In a medium bowl, combine lettuce and radishes. Dress lightly with oil, vinegar, salt, and pepper. Place chicken in a medium bowl, taste, and if desired, season with salt and pepper. Set the queso fresco, salsa, and lime wedges out in bowls along with the chicken, salad, and tortillas. Allow each person to assemble tacos as desired.