Butterfly the chicken if it is thicker on one end than the other (it usually is). Pat the chicken dry with a paper towel, and salt and pepper each side.
In one medium-sized bowl, beat the egg. In another bowl, combine the pecans and flour.
Heat oil (cover the bottom of the pan) in a large skillet over medium heat. Once the skillet is hot, turn the heat down to a lower setting, somewhere between medium and low. Now, dip the first piece of chicken in egg, then coat in crumbs, using the back of a spoon to really press the nuts into the chicken. Place gently in pan. (It should sizzle right away; if it doesn't, take it out and increase the heat.) Repeat with the remaining chicken.
Don't flip it over until you can easily see some white (cooked) meat around the edges. Carefully turn each piece over. You may want to add a little more oil to prevent the pecans from scorching. Cook a few more minutes, and cut into the center of the thickest to check for doneness.