Evenly cut the chicken breasts in half through their thickness. Lay your hand flat on top of the breast, knife hand off the edge of the board. Keeping your blade level, glide your knife through the thickness of the breast until you're clear through it.
Heat a large skillet (preferably stainless or cast iron) on medium heat until quite hot, but not smoking. Meanwhile, season the chicken with salt and pepper. Place the flour in a wide bowl or on a plate.
Add about 2 Tablespoons of oil to the skillet. Using tongs, dredge a chicken breast in the flour, shake off the excess and place in the skillet, best looking side down. Repeat with the others immediately. Don't crowd the skillet, if necessary, cook in batches. Add more oil as needed.
Allow the chicken to cook, undisturbed for 2-4 minutes. It will usually stick while it's first cooking then release when it's ready to flip. Test it by wiggling it with tongs. When it's golden brown and the chicken has cooked up the sides, turn it over. You shouldn't be prying it up from the pan.
Cook the second side about 2 minutes until the chicken is golden and just cooked through. Remove to a platter and cover.