When you want to broil a chicken breast consider this:
A bone-in, skin-on chicken breast half is thicker at one end than the other, so under the broiler, the thinner part will dry out before the thicker is cooked. Even worse, the chicken may scorch before cooking through.
A skinless, boneless chicken breast is a nice even cut, but even it can dry out under the intense heat of the broiler, that’s why our favorite method is to wrap a skinless boneless chicken breast in bacon or pancetta before broiling. The fatty meat protects the chicken and adds amazing flavor. Another approach is to use a yogurt marinade, it will form a protective crust and give a good color to the cooked chicken. Try this recipe, cooking under the broiler rather than on the grill. Or use a sweet sticky glaze -- like this spicy apricot recipe -- to protect the chicken.
For the simplest approach to broiling a chicken breast, think thin and use a chicken cutlet. Simply seasoned and brushed with oil, chicken cutlets can be broiled much as you might grill them. Cutlets also take well to marinading before broiling.
Preheat the broiler with the rack six inches from the heating element. Rinse and pat the chicken dry, then season with salt and pepper and brush lightly with olive oil or a neutral oil such as canola. Alternatively, squeeze lemon juice over the chicken. Place on a foil-lined broiler pan, on a baking sheet, or in a cast-iron skillet.
Remember that broilers vary in heat intensity; move the rack to a lower position if the chicken is browning too quickly, or to a higher rack if too slowly. In case things are cooking unevenly, remove items from the broiler pan or baking sheet as done.