Prep - Heat vegetable oil in a small pot over medium-low heat. Add garlic to pot and cook until fragrant, about a minute. Pour in vinegar, ketchup, and honey; bring to a boil. Reduce heat to low and let it sauce bubble and reduce for at least 20 minutes, until honey balsamic sauce is thick and sweet.
Combine - Thread chicken and vegetables onto skewers. You might have a few extra pieces of vegetables, just make another veggie-only skewer. Season chicken kabobs on all sides with salt and pepper.
Spray cold grates of grill with grilling spray and heat to medium heat.
Grill chicken kabobs until charred on all sides and chicken is cooked through (180°F), about 15 minutes, turning occasionally.
Create - During the last few minutes of grilling, brush honey balsamic sauce all over the chicken kabobs, turning occasionally to lightly caramelize the sauce. Remove honey balsamic chicken kabobs from grill and serve.