Rinse chicken breasts and pound to 1/2-inch thickness using a meat mallet. Cut each chicken breast in half.
Place flour in a bowl. Beat eggs in a separate bowl until light in color. Pour crushed pretzels onto a jelly roll pan.
Dip each chicken breast in flour, then in beaten eggs, then coat with pretzels. Place on a separate plate.
Heat oil in a deep skillet over medium-high heat. Cook chicken breasts in batches until golden brown and crispy, 3 to 4 minutes per side. Add more oil between batches if needed.