Arrange one of the chicken breasts between two pieces of parchment or wax paper. Using a meat tenderizer (or the bottom of a heavy skillet), pound the chicken breast until it is 1/4-inch thick. Repeat the pounding process with the remaining chicken breasts.
Add the flour to a shallow dish then season it with salt and black pepper.
Whisk the eggs in a second shallow dish.
Add the breadcrumbs to a third shallow dish.
Line a baking sheet with paper towels.
Dredge the chicken in the flour, shaking off any excess then dip it in the egg wash and finally in the breadcrumbs, pressing to adhere them on all sides. Repeat the breading process with the remaining chicken breasts.
Generously coat a large skillet with oil then place it over medium heat. Once the oil is hot, add the chicken and cook until golden brown and crispy, 3 to 5 minutes, then flip it once and continue cooking until it is cooked through.
Transfer the chicken breast to the paper towel-lined plate and immediately season it with salt. Repeat the cooking process with the remaining chicken breasts then serve.