Thaw and trim chicken breasts. Pat down with a paper towel and cut into 1 1/2-2" chunks. Then place in a glass bowl or zip top bag. Add the bell peppers. Then add the olive oil, balsamic vinegar, Dijon mustard, garlic, salt and pepper. Toss until it is mixed well. Place in the refrigerator for at least 30 minutes.
Preheat grill to medium-high heat.
Thread chicken and bell peppers through skewers. Alternate the chicken and peppers until everything is used up. Then place on the grill for 5 to 6 minutes per side (or until a thermometer reads 160° to 165°F and the center is no longer pink).
Other vegetables you can add to the chicken kabobs:
Note: Some of the softer vegetables like zucchini and tomatoes will end up cooking faster. I'd recommend putting those on their own skewer so you can remove them from the grill when they are cooked.