1) Thinly slice the chicken into long, very thin, bias-cut strips. Set aside. 2) Pour oil into a heavy medium pot to come three-fourths of the way up the sides. Heat over medium to 350˚F. 3) While the oil is heating, prepare the batter: In a medium metal bowl, whisk the flour, black pepper, zest, lemon juice, and 11⁄2 cups cold water. 4) Add the ice-cubes, as tempura batter fries up better when it is cold. Add the strips of chicken and coat them with the batter. 5) Add the coated chicken strips, a few at a time, and fry them, turning occasionally, until golden-brown. Remove with a slotted spoon and drain on paper towels. Sprinkle with salt. 6) In a small bowl or container, mix the mayonnaise with the chopped dill, stirring to combine. 7) Serve the warm chicken strips with the dill mayonnaise.