Prepare the grill for cooking over medium-high heat. Place the dressing ingredients and a tablespoon of water in a blender and process until smooth.
Slice each chicken breast lengthwise into 4 strips. Place the pieces in a large bowl, sprinkle with the barbecue rub, and toss to coat them evenly. Set aside.
Mist each bread slice with cooking spray and sprinkle with the garlic powder. Grill them over indirect heat until lightly browned, about 2 minutes each side. Cut them into 1-inch cubes.
Generously oil the grill grates. Grill the chicken until no longer pink, about 5 minutes per side. Next, grill the romaine, cut sides down, over indirect heat until grate marks start to appear, about 2 minutes. Set each half on a serving plate.
Slice the chicken into bite-size pieces. Evenly distribute half the dressing (serve the rest on the table) and the chicken and croutons among the romaine portions.