Pound the chicken breasts to an even thickness. You do not want them to be too thin, simply uniform in thickness. Place a breast between two pieces of waxed paper or plastic wrap, or in a resealable plastic bag. Starting in the center and working out to the edges, pound lightly with the flat side of a meat mallet or the bottom of a heavy pan until the chicken is even in thickness.
Mix 1 teaspoon salt and 1/2 teaspoon ground black pepper with 1/2 cup all-purpose flour.
Quickly dredge the chicken breasts in the flour, so that they are just lightly dusted with flour.
Heat a sauté pan that has a lid over Medium-High heat. When it is quite hot, add 3 tablespoons of olive oil and 2 teaspoons butter. Once melted, swirl the pan to coat the bottom evenly.
Reduce heat to Medium. Add the chicken breasts. Cook for about 1 minute to help them get a little golden on one side—not long enough to actually sear or sauté, only to heat them. Carefully turn over each chicken breast.
Reduce heat to Low. Apply the lid. Set a timer for 10 minutes and walk away. Do not lift the lid; do not peek.
After 10 minutes, turn off the heat. Still, do not peek! Reset the timer for 10 minutes and leave the chicken breasts in the pan. Again, do not lift the lid and I repeat, do not peek.
When the second 10 minutes are up, take the lid off and behold the wonder: Soft, tender, juicy chicken breasts that are not dried out. Check to make sure there is no pink in the middle, especially if the breasts are thick. To be absolutely sure your chicken is cooked well, use an instant-read thermometer to check (the chicken should be at least 165°F). Slice, serve, and enjoy!