Remove any fatty areas or excess skin from chicken breasts. Either marinade whole breasts for 2 hours or to speed the marinade time up, cut chicken into 1" pieces and marinade for 30 - 60 minutes.
Mix all chicken ingredients together in a bowl or reusable bag and let marinade for 30 minutes - 1 hour. Use some of this time to prepare dressing and salad ingredients. If using 1" pieces and you plan on grilling the chicken as kabobs, soak the wooden skewers in water while the chicken is marinating to keep them from burning.
Add all dressing ingredients to a small glass jar and shake to combine. Start by adding only 1 Tbsp. of water and add an additional Tbsp. if needed to reach desired consistency (amount of water will depend on tahini thickness).
Prepare all salad ingredients and add to a serving bowl. Set aside.
Preheat Grill to about 425° F (218° C) and brush and oil grill grates.
If using 1" chunks, skewer chicken onto kabob skewers leaving a few millimeters of space between each chunk so that chicken cooks evenly. Once grill is hot, place chicken on grill and cook for 5-8 minutes per side for breasts or 4-6 minutes per side for kabobs.
Remove chicken from grill and let sit for 5-10 minutes before slicing breasts (if cut into chunks, it does not need to rest).
Shake salad dressing jar and pour over prepared salad. Toss to combine.
Add chicken to salad and serve immediately.