Preheat your grill to medium-high heat and preheat the oven to 425°F (220°C).
For the chicken, pat the breasts dry with paper towels. Rub each breast with olive oil and season with salt and pepper.
Grill the chicken for 6-7 minutes per side or until the internal temperature reaches 165°F (75°C). Once cooked, let it rest for 5 minutes.
While the chicken grills, prepare the chimichurri sauce by combining parsley, garlic, oregano, olive oil, red wine vinegar, chili flakes, salt, and pepper in a bowl. Mix well and set aside to let the flavors meld.
Toss the zucchini, bell peppers, and red onion with olive oil, thyme, salt, and pepper. Spread them on a baking sheet in a single layer.
Roast the vegetables in the preheated oven for 20 minutes, or until they are tender and have a slight char.
Slice the rested grilled chicken and serve with a generous drizzle of chimichurri sauce and a side of the roasted vegetables.