Cut the chicken breast into 2 pieces (from side to side) Pound each half to flatten out to be about 1/4 inch thick. Take about 1 tablespoon and brush the top of each chicken breast with the olive oil and sprinkle about 1 teaspoon over top of the 4 chicken breast patties. Turn the breast over and repeat the process.
Cover and set in the refrigerator for 1 to 2 hours.
Heat 2 tablespoons of olive oil to a cast iron skillet and fry the chicken breast on each side for 2 1/2 to 3 minutes on each side or until the chicken is no longer pink inside. Add additional olive oil while frying as needed.
While the chicken is in the refrigerator prepare the basil mayonnaise. In a mini food processor add the mayonnaise, fresh basil, garlic, olive oil, and lemon juice process until the ingredients are well blended.
To assemble: Using your favorite bun place the chicken breast on the bun spread the top of the bun with the basil mayonnaise.
Optional add lettuce and fresh sliced tomatoes to the sandwich if desired.