Put a skillet on at medium high and swirl in enough olive oil to coat the bottom.
Lightly salt, pepper and garlic powder one side of the chicken filets. Put the filets in the skillet seasoned side down and season the up side.
Cook 2 to 4 minutes a side depending on the thickness. When the juices run clear and/or they are firm to a poke and/or they read 175° on a meat thermometer remove them to a dish that will catch the drippings.
While the chicken is cooking coarsely chop up the basil leaves.
Add about three tablespoons of butter to the skillet. As soon as the butter has melted add the basil leaves. Stir the basil around with a wooden spoon scraping the bits from the chicken off the bottom and getting the leaves mixed with the butter.
Put the filets on the serving plates and spoon some of the butter and basil mixture on top.