Preheat your oven to 400°F (200°C).
Place the cherry tomatoes on a baking sheet, drizzle with half of the olive oil and a pinch of salt and pepper, then roast for 15 minutes until they begin to burst.
Bring a small pot of salted water to a boil and cook the whole wheat penne according to package directions until al dente; reserve 2 tablespoons of pasta water before draining.
While the pasta cooks, season the chicken breast with oregano, salt, and pepper. Heat the remaining olive oil in a skillet over medium-high heat and sear the chicken for 5-7 minutes per side until cooked through, then slice into strips.
In a small bowl, whisk together the Greek yogurt, grated parmesan, and minced garlic, slowly adding the reserved pasta water to reach a creamy consistency.
Return the cooked pasta to the skillet over low heat, add the yogurt sauce, spinach, roasted tomatoes, and chicken, tossing gently until the spinach is wilted and the sauce coats everything evenly.