The secret to this light and tangy dish is a marinade that's made with Italian vinaigrette. It comes together quickly, and the chicken strips are so flavorful you may find you don't even need dressing for the salad.
Combine the marinade ingredients in a medium-size bowl and whisk them to blend. Set aside 1/2 cup of the mixture for basting the chicken on the grill.
Place the chicken breasts in a gallon-size zip-lock bag and pour in the remaining marinade. Press the air out of the bag and seal it. Turn the bag to thoroughly coat the chicken, then place it in a bowl and refrigerate it for at least 1 hour, turning it occasionally. Remove the meat from the refrigerator 20 minutes before grilling.
Prepare a charcoal fire or set a gas grill to medium-high, close the lid, and heat until hot -- about 10 to 15 minutes.
Remove the chicken from the bag and discard the marinade. Grill it uncovered, basting with the reserved marinade. Cook the chicken until it is no longer pink inside, about 2 minutes per side on a gas grill. Transfer the breasts to a cutting board and let them rest about 5 minutes before thinly slicing them crosswise. Serve the chicken over salad greens and cherry tomatoes. Serves 6 to 8.