Coarsely chop ½ cup blueberries and place in a small bowl with remaining 1 cup whole blueberries. Add pineapple, cilantro, chutney, lime juice, jalapeno and ¼ tsp salt; toss to combine. Cover and chill until ready to serve.
Preheat grill to medium-high. Rub chicken cutlets evenly with 1 Tbsp oil.
In a small bowl, mix jerk seasoning and ½ tsp salt; sprinkle mixture evenly onto both sides of chicken.
Brush 1 Tbsp oil on grill grates and place chicken on grates. Grill, uncovered, until grill marks appear and chicken is cooked through, about 3 – 4 minutes per side. Remove chicken from grill; cover and let rest 10 minutes.
Slice or shred chicken. Divide evenly among lettuce leaves. Spoon blueberry salsa onto chicken. Garnish with cilantro leaves if desired.