Mix marinade ingredients in a bowl. Put chicken in a zip close style 1-quart freezer bag. Pour half of marinade into bag with chicken. Remove as much air as possible and seal. Squish marinade around chicken in bag. Place in the refrigerator for several hours.
Wash vegetables and chop peppers and onions into pieces about 1 ½” leaving mushrooms whole. Marinate vegetables with the other half of the marinade in another bag for at least 30 minutes.
Alternate chicken and veggies on kabob skewers. Discard chicken marinade and reserve veggie marinade. Grill until chicken is done, basting with leftover vegetable marinade. You may also broil kabobs in the oven. Broil 10 minutes, flip kabobs and broil 5-10 minutes more until chicken is done. Keep an eye on them. If the veggies seem to be cooking too fast for the chicken, lower rack from heating element and flip often.
Serve over rice.