Preheat the grill to medium-high heat.
Grill the chicken breast strips until cooked through and slightly charred, about 6-8 minutes per side.
Remove chicken from grill and cut into thin strips if not already sliced.
Toss grilled chicken strips with sweet and tangy BBQ sauce and pineapple chunks to coat evenly.
Warm the flour tortillas briefly on the grill or in a pan until soft and pliable.
Lay a tortilla flat and layer shredded lettuce, diced red onion, sliced red bell pepper, and a sprinkle of shredded cheddar cheese.
Top with the BBQ chicken and pineapple mixture.
Roll the tortilla tightly into a wrap.
Cut each wrap in half diagonally and arrange two halves in a staggered stack on a white rectangular plate.
Serve with a small ramekin of extra BBQ sauce on the side.