Preheat the oven to 400°F.
Slice the zucchini lengthwise into noodles using a spiralizer or vegetable peeler and place on a baking sheet.
Drizzle half of the olive oil over the zucchini noodles, and sprinkle with salt, pepper, and dried oregano. Toss to coat evenly.
Roast the zucchini noodles in the oven for 10-12 minutes until tender.
While the zucchini roasts, season the chicken breast with salt, pepper, and dried basil. Grill or pan-sear the chicken over medium heat until cooked through (internal temperature of 165°F), about 6-7 minutes per side. Let the chicken rest, then slice into strips.
In a pan, heat the remaining olive oil over medium heat. Add minced garlic and sauté until fragrant, about 1 minute.
Add the burst cherry tomatoes and spinach to the pan with garlic. Cook for 2-3 minutes until the tomatoes are warmed and the spinach begins to wilt.
Combine the roasted zucchini noodles with the tomato and spinach mixture in a large serving bowl, and gently toss.
Top the dish with sliced grilled chicken. Adjust seasoning with additional salt and pepper if needed, and serve warm.