Preheat your grill or a skillet over medium heat.
In a small bowl, mix the olive oil, garlic powder, paprika, salt, and pepper. Rub this mixture over the chicken breasts.
Grill the chicken for about 6-7 minutes on each side, or until cooked through and no longer pink in the center. Remove from heat and let it rest for a few minutes before slicing.
In another bowl, combine the mashed avocado with lime juice and cilantro (if using). Season with salt to taste.
Spread butter on one side of each slice of bread. On the unbuttered side, layer the sliced chicken, avocado mixture, and shredded cheese.
Top with another slice of bread, buttered side up.
Grill the sandwich for about 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove from the skillet, slice in half, and serve warm.