Preheat the grill to medium-high heat (about 400°F or 200°C).
In a small bowl, combine olive oil, garlic powder, paprika, salt, and black pepper to create a marinade.
Brush the chicken breasts evenly with the marinade on both sides.
Place the chicken breasts on the preheated grill.
Grill the chicken for 6-7 minutes on each side, or until the internal temperature reaches 165°F (74°C) and the chicken is cooked through.
While the chicken is grilling, prepare the vegetables for steaming.
Fill a pot with about 1 inch of water and bring it to a boil over medium-high heat.
Place a steamer basket in the pot, making sure the water does not touch the bottom of the basket.
Add broccoli florets, sliced carrots, and zucchini to the steamer basket.
Cover the pot with a lid and steam the vegetables for 6-8 minutes, or until they are tender but still crisp.
Remove the steamed vegetables from the pot and transfer them to a serving bowl.
Add unsalted butter, salt, and black pepper to the vegetables and toss gently until the butter is melted and the vegetables are evenly seasoned.
Remove the grilled chicken from the grill and let it rest for 3-5 minutes before serving.
Serve the grilled chicken breasts alongside the steamed vegetables.