Our friends at The Kitchn offer a method that they say makes "unfailingly juicy and succulent" breasts. They say it came from the old Joy of Cooking, which gave it a special label: 'Cockaigne' - reserved for only their personal favorite and best recipes.
Moist and Tender Chicken Breasts
2-4 boneless, skinless chicken breasts, of even thickness
Salt and pepper
1/4 cup flour
Handful of herbs (optional)
Olive oil and butter
If you have a little time before cooking dinner, lightly salt and pepper the chicken breasts. It's great if you can do this the night before, but it's not necessary.
Mix about a half teaspoon of salt in with the flour along with a little pepper. Chop the herbs finely, if using, and mix in as well.
Dredge both sides of the chicken lightly in the flour.
Heat a large heavy skillet (with a lid) over medium high heat, with a little olive oil and about half a tablespoon of butter. Quickly sear both sides of the chicken breast until just faintly golden; you don't want the insides to cook much at all.
Cover tightly and turn the heat down very low. Cook for 10 minutes without lifting the lid. Remove from the heat and let sit for another 10 minutes, still tightly covered.
Remove lid and serve. There is usually just enough chicken fat, along with pan juices, to make a simple sauce, too.