First, marinate the chicken. Begin by slicing the chicken breasts into 1.5-inch to 2-inch cubes and place them into a large gallon size bag or a deep dish with sides. Set them aside.
Now make the chicken marinade. Add the soy sauce, Worcestershire sauce, lime juice, orange juice, honey, garlic, ginger, salt, olive oil, rice vinegar, and sriracha (if using). Whisk all the ingredients together until the honey dissolves.
Pour the chicken marinade over the chunks of chicken and mix the chicken with the marinade. Seal the bag and place the chicken in the refrigerator for at least 30 minutes to for up to 2 hours.
Next, prepare the veggies. Place the chopped peppers, purple onion, and garlic cloves into a large bowl. Set aside.
Make the veggie marinade and add the olive oil, sesame oil, lime juice, garlic, ginger, salt, rice vinegar, cilantro, and honey to a mason jar. Cover the jar and shake until combined.
Pour the marinade over the veggies and toss until coated. Set aside for later.
Preheat the grill to 400ºF.
Assemble the chicken kabobs. To assemble the kabobs, use water soaked wooden skewers or metal skewers. Thread a piece of chicken onto the skewer, then a bell pepper, onion, and garlic clove. Repeat until you have 3 or 4 pieces of chicken on the skewer. Set the kabob aside and repeat until all the ingredients have been placed on kabobs.
Place the kabobs on the grill and turn them every 5-7 minutes for 25-30 minutes or until the chicken has an internal temperature of 165ºF.
Remove from the grill and let the chicken rest for 5 minutes. Serve with freshly squeezed lime juice and fresh cilantro.