Begin by preparing the chicken. Slice the chicken breasts into strips or bite-sized pieces.
Set up a breading station: In one bowl, combine the flour, salt, and pepper. In a second bowl, beat the eggs. In a third bowl, place the panko breadcrumbs.
Dredge each piece of chicken in the flour mixture, shaking off the excess. Then dip it into the beaten eggs, and finally coat it with the panko breadcrumbs, pressing gently to adhere.
In a large skillet, heat the vegetable oil over medium-high heat. Once hot, carefully add the breaded chicken pieces in batches, ensuring not to overcrowd the pan. Fry until golden brown and cooked through, about 4-5 minutes per side. Remove and drain on paper towels.
While the chicken is frying, prepare the sauce by whisking together the mayonnaise, sweet chili sauce, sriracha, and lime juice in a small bowl. Adjust the spice level to your preference.
Serve the crispy chicken hot, drizzled with the bang bang sauce or serve the sauce on the side for dipping.