Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Dice the zucchini, red bell pepper, and red onion into uniform, bite-sized pieces.
Place the chicken breast and the chopped vegetables onto the prepared baking sheet.
Drizzle everything with olive oil and sprinkle evenly with dried oregano, sea salt, and black pepper.
Roast in the oven for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
While the chicken roasts, grate the cucumber and use a clean kitchen towel to squeeze out all excess moisture.
In a small mixing bowl, combine the Greek yogurt, squeezed cucumber, minced garlic, lemon juice, and chopped fresh dill.
Allow the chicken to rest for 5 minutes before slicing it into strips.
Serve the herb-roasted chicken and vegetables warm with a generous dollop of the fresh tzatziki sauce on the side.