Preheat the grill or grill pan over medium-high heat.
In a mixing bowl, combine the olive oil, garlic powder, paprika, salt, and pepper. Coat the chicken breasts evenly with this mixture.
Grill the chicken for about 5-7 minutes on each side or until fully cooked and internal temperature reaches 165°F (75°C). Remove from the grill and let rest for a few minutes before slicing.
While the chicken cooks, slice the avocados in half, remove the pit, and scoop the flesh into a bowl. Mash gently with a fork and stir in lime juice, salt, and pepper to taste.
Once the chicken has cooled, slice it into strips.
Lay out the tortillas on a clean surface. Spread about 1/4 of the mashed avocado on each tortilla.
Add a portion of grilled chicken, cherry tomatoes, shredded lettuce, and cheese on top of the avocado for each wrap.
Carefully roll each tortilla tightly, tucking in the sides as you go to create a wrap. Wrap in aluminum foil or parchment paper if desired for easier handling.
Serve immediately with salsa or hot sauce on the side, if using.