Dissolve 1/4 cup of salt into 1 quart of water in a baking dish. Place chicken breasts in brine and let soak for 30 minutes.
Make sure grill is clean and spray with a little non-stick cooking spray. Start your charcoal grill with coal piled on just one side of grill. If using gas grill, just heat one side on medium high.
Remove chicken from brine after 30 minutes and pat dry. Coat with olive oil and add salt and pepper.
Place chicken over hot coals or burners and grill for approximately 1.5 minutes or until 1st side is browned. Flip over and grill 2nd side for another 1.5 minutes.
After both sides have browned nicely, move chicken to side of grill without heat on or charcoal, cover grill, and let chicken cook another 5-7 minutes. Internal temperature should be 165 degrees F.