Slice chicken breasts into thin slices. You can do thin strips lengthwise or cut through the thick part and make 2 thin chicken breast slices. Either way works fine.
Place chicken into a gallon size zip to bag.
Make the Italian Dressing by adding the olive oil, red wine vinegar, lemon juice, spicy brown mustard, honey, parmesan cheese, herbs and spices to a mason jar.
Cover the jar and shake vigorously until well combined.
Pour half of the dressing over the chicken.
Press the air out of the bag and seal. Turn the bag over a few times, rubbing the dressing all over the chicken.
Refrigerate at least one hour and up to 8 hours before grilling.
Prepare a grill fire to 325° with pecan or hickory for smoke flavor.
Thread chicken and zucchini onto skewers.
Grill chicken and zucchini skewers over indirect fire with the grill closed.
Cook for 15 minutes, check the chicken in several places using a digital thermometer, continue cooking until chicken reaches 165°.
Remove from grill to a serving platter.
Slide the chicken and zucchini off of the skewers for serving and drizzle with remaining Italian dressing if desired.