Mix 2 tablespoons olive oil, 1/2 teaspoon smoked paprika, 1/2 teaspoon salt and 1/4 teaspoon pepper together in a small bowl. Massage all over chicken and let rest 15-30 minutes (time permitting) at room temperature before grilling. (You may also let marinate in refrigerator up to overnight then bring to room temperature before grilling.) Meanwhile, grease and preheat the grill to medium heat, 375-450°F.
Grill chicken undisturbed for 5-8 minutes per side depending on thickness, or until chicken is cooked through. (An inserted thermometer should read 155 degrees F.) Remove chicken from grill and let rest 5 minutes before chopping. Add chicken to a bowl and toss with 1/4 cup barbecue sauce or enough to generously coat.
To assemble, add the Salad Ingredients and chicken to a large bowl and toss to combine. If you don’t expect leftovers, drizzle salad with desired amount of dressing and toss to combine. Garnish with tortilla strips. If you do expect leftovers, garnish individual servings with Dressing and tortilla strips.