Preparing the Grill. For just steps for making the chicken, just do steps 7 to 19.
Preheat the grill on the highest temperature setting for about 10 minutes (to roughly 500°F).
After the grill is preheated, scrape any remaining bits with a wire grill brush.
Fold a paper towel in half, and in half again, then roll it up into a tight roll.
Hold the paper towel with tongs and dip in the oil to oil the grill bars. Don't use too much oil or you'll have flare-ups.
Three rules to great grilling: keep it hot, keep it clean, keep it lubricated. (Source: Steven Raichlen)
Preparing the Chicken
Wash your hands thoroughly and frequently when handling raw chicken.
If not marinated, rinse the chicken in cold water.
Pat dry with paper towels.
Trim any fat, if you so desire.
Holding the breast flat, cut the chicken in half evenly with the knife parallel to the board. KEEP YOUR FINGERS UP AND OUT OF THE WAY!
Here's another view of how to cut.
Afterwards you'll have twice as many pieces.
Sprinkle coarse salt and grind black pepper on both sides, if you wish.
Use 2 visually distinct pairs of tongs. One for raw meat, one for cooked.
Cook 2-4 minutes per side on your highest grill setting.
When the edges are white, it's time to flip.
Cook until done. You can check by inserting an instant read thermometer into the thickest part. It should read 165°F (source: foodsafety.gov).
Brush off the big pieces left from cooking.
Added benefits: 1) Eat less. Even if you have 2nds, your only eating 1 breast. 2) Perfect for sandwiches.