To make the dipping sauce, combine all ingredients in a bowl and divide between four small dipping bowls.
Sprinkle the chicken breasts with salt and pepper. Spread the flour on a plate, the breadcrumbs on another plate, and the eggs in a shallow bowl (beat the eggs). Dredge each chicken breast in the flour, then the eggs, then coat evenly with the bread crumbs. Be careful not to press the breadcrumbs into the chicken.Heat the oil over medium-high heat in a large frying pan until very hot but not smoking. Add the breaded chicken breasts and reduce the heat to medium. Fry the chicken for about 4 minutes on each side until golden brown and the chicken feels firm when pressed in the center. Turn down the heat if necessary to prevent burning.Transfer the chicken breasts to a cutting board and slice across the grain into wide strips. Transfer to individual serving plates and serve immediately with the dipping sauce.