Preheat your grill to 300°F.
Cut slits about 1 in. deep and 1/2 in. apart into each chicken breast. Do not cut all the way through.
Insert mozzarella cheese and a slice of bacon into each slit. Then, season the chicken breasts with chili powder and oregano.
Place the chicken breasts on the grill and close the lid. Grill for 30 to 45 minutes until the chicken reaches an internal temperature of 165°F.
Slice each avocado in half lengthwise and remove the pit. Brush the interior of the avocados with olive oil and season with salt and pepper to taste.
Once the chicken breasts are fully cooked, move them to the top warming rack. Place the avocados face side down on the grill. Grill for 30 seconds.
Remove the chicken breasts and avocados from the grill. Let the chicken rest for five minutes before serving. Enjoy!