Whisk all of the marinade/dressing ingredients in a glass mixing bowl. Pour out/separate half of the marinade into a large, shallow dish. Refrigerate the remaining marinade to use as the dressing later.
Add the chicken to the marinade in the bowl; marinade chicken for 15-30 minutes (or up to two hours in the refrigerator if time allows). Meanwhile, prep all the veggies for the salad and place them on a large platter or bowl.
Once chicken is ready, heat 1 tablespoon of oil in a grill pan or a grill over medium-high heat. Grill chicken on both sides until browned and completely cooked through.
Allow chicken to rest for 5 minutes; slice and arrange over salad. Drizzle salad with the remaining dressing and mix well. Serve with lemon wedges.