Trim and cube the chicken breast. Cut the bell peppers and onion into similar sized pieces. Place the chicken in one large Ziploc bag and the vegetables in a second Ziploc bag.
In a small bowl, whisk together the tomato paste, oil, soy sauce, honey, water, smoked paprika, and garlic. Season with salt and pepper, to taste. Reserve 2 tablespoons of marinade.
Pour half of the remaining marinade over the chicken in the bag and the other half over the vegetables. Seal the bags and shake to distribute the marinade over the chicken and vegetables. Allow the chicken and vegetables to marinate for a minimum of 30 minutes in the refrigerator (we like to marinate ours for about 2 hours).
While the chicken and veggies marinates, soak the wooden skewers in water for 20-30 minutes (this will prevent them from burning when on the grill).
Preheat the grill to medium-high heat. Pour the marinated veggies onto a plate. Push the veggies onto the skewers, leaving about an inch of space at the top and bottom of the skewers and about ½ inch of space between the veggies. Repeat this process until all of the veggies are on the skewers. You can brush any remaining marinade over the vegetables, if desired.
Pour the marinated chicken out on the same plate. Push pieces of the chicken onto the skewers, leaving about an inch of space at the top and bottom of the skewers and about ½ inch of space between the pieces of chicken. Repeat this process until all of the chicken is on the skewers. Discard any remaining marinade.
Place the skewers on the preheated grill and cook on one side, undisturbed, for about 4 minutes. Turn the skewer over and repeat on the other side for about 4 minutes. Remove the chicken and vegetables from the grill and brush with the reserved marinade. Serve and enjoy!