1. Preheat the grill to high heat. Place the chicken between two sheets of plastic wrap or waxed paper on a cutting board. Using the flat head of a meat mallet (or a rolling pin), pound the chicken until it is 1/2 inch thick. Rub each breast with the olive oil, salt and pepper. Grill 3 to 5 minutes per side, or until cooked through. Let chicken cool.
2. Whisk together the vinegar, mustard and honey. Slowly whisk in the oil. Stir in the basil and season with salt and pepper. Chop the chicken and transfer it to a medium bowl. Mix in the barbecue sauce and stir to coat. In a large serving bowl, toss the lettuce, tomatoes, cucumber, zucchini, cheddar, red onions, and dressing. Top with the chicken and serve.