Usually, I bake or saute chicken. The other day, I tried it under the broiler and it turned out very well and quite close to actual BBQ style.
I used boneless, skinless chicken breasts. Trimmed the tiny bit of non-meat part and sliced it in two. Then coated it with olive oil. salt, black pepper, garlic powder (there is more, but read on).
Placed them in a pan about 3-4 inches from the broiler element, on high. Three or four minutes on a side with one flip. I like oregano on this but add that right before the flip so it does not burn.
A minute before you take it out, add a splash of vinegar or lemon juice (the acid goes really well here).
This will cook quickly so you want it nice and broiled but not dried out or burned and placement near the broiler element is important.
Of course you can spice it to your taste, but this is plain and simple and quite tasty.