Flatten chicken breast halves to no more than 1/2 inch thick.
Whisk olive oil, lemon juice, pepper sauce and thyme. Season with salt and pepper. With 2 tablespoons of the marinade, marinate chicken breasts for at least 30 minutes (and no more than 4 hours).
Warm remaining dressing.
Grill chicken and onion slices, ~4 minutes per side.
Separate onion rings, slice chicken. Arrange over lettuce and sprinkle with feta.