Slice the chicken breasts into 1/2-inch wide strips.
Season the chicken strips evenly with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Set up a breading station with three shallow dishes: put the 1/2 cup flour in the first, beat the egg with 2 tablespoons milk in the second, and combine 3/4 cup shredded coconut with 3/4 cup breadcrumbs in the third.
Dredge each chicken strip in flour, shake off excess, dip into the egg mixture, then press into the coconut-breadcrumb mixture to coat thoroughly.
Heat enough vegetable oil in a large skillet over medium heat to shallow-fry (oil should be hot but not smoking).
Fry the breaded chicken in batches, turning as needed, until golden brown and cooked through, about 3–5 minutes per side depending on thickness.
Transfer cooked chicken to a paper-towel-lined plate to drain, then serve hot.
