Trim fat and connective tissue from the chicken breast halves.
Slice each half horizontally to form two cutlets.
Pound the cutlets between two pieces of plastic wrap or waxed paper until they are uniformly thin, about 1/4 to 1/3 inch.
Season the cutlets with 1/2 teaspoon garlic salt and 1/8 teaspoon pepper, and set aside.
Mix 1/2 cup all-purpose flour with 1/2 teaspoon garlic salt and 1/4 teaspoon pepper in a shallow dish or pie plate. Set aside.
Cut the lemon into wedges. Thinly slice the cheese. Dice or thinly slice the tomato. Dice or thinly slice the avocado. Set aside.
Preheat a large, heavy skillet over medium high heat for 5 minutes.
Meanwhile, dredge each chicken cutlet in the seasoned flour.
Make sure each piece of chicken is well coated, and shake away the excess.
Pour the Corn Oil in the preheated skillet. Add the seasoned, floured chicken breast cutlets.
Brown the chicken for about 3 minutes on each side, or until it reaches an internal temperature of 165 degrees.
Remove skillet from heat. Squeeze the juice from 3 lemon wedges over the 6 pieces of chicken.
Working quickly, arrange the toppings: first cheese, then avocado, then tomato. Season the toppings lightly with garlic salt and pepper.
Place a lid on the skillet, and wait a few minutes for the cheese to melt.
Serve California Chicken with additional lemon wedges.