Marinate Chicken in Lemon Juice Olive Oil, chopped Thyme, Salt, and Pepper for (at least) 30 minutes.
Prep your grill (or pan).
Clean, remove stem, and cut a slit into the pepper; remove any seeds, and open inside out, to optimize grilling. Brush with Olive Oil, sprinkle with salt.
Place Chicken Breast on the Grill for 10-15 minutes a side. After turning the chicken, place peppers on grill. Allow to cook for about 5 minutes, watch for blistering.