Trim the chicken breasts and slice each into strips about 3 3/4 inches long, 1/2 inch wide, and 1/4 inch thick; avoid slicing thinner than 1/4 inch.
Set up three shallow bowls: place the flour in the first, beat the eggs in the second, and combine the breadcrumbs, paprika, garlic powder, onion powder, salt, and black pepper in the third.
Heat vegetable oil in a deep fryer or heavy skillet to 350°F (use a cooking thermometer) and maintain that temperature.
Working in batches, dredge each chicken strip in flour and shake off excess.
Dip the floured strip into the beaten eggs, coating completely, then press it into the breadcrumb mixture so the crumbs adhere.
Carefully lower the coated strips into the hot oil using tongs and fry for 4–5 minutes per batch, until golden brown and cooked through.
Remove the chicken fries with tongs or a slotted spoon and drain on paper towels, then serve immediately with your preferred dipping sauce.