Preheat your oven to 400°F (200°C).
Place cherry tomatoes on a baking sheet, drizzle with olive oil, and sprinkle with a pinch of salt and pepper. Roast for 15 minutes until the skins are blistered and juicy.
While tomatoes roast, bring a pot of salted water to a boil and cook the chickpea spaghetti according to package instructions. Reserve 2 tablespoons of the pasta water before draining.
Season the chicken breast with salt and pepper, then grill or pan-sear over medium heat until cooked through. Let it rest for 3 minutes before slicing into thin strips.
In a small bowl, whisk together the Greek yogurt, minced garlic, lemon juice, and the reserved pasta water until smooth and creamy.
Return the drained pasta to the pot over low heat. Pour in the yogurt sauce and toss gently until the pasta is well-coated.
Fold in the roasted tomatoes and sliced chicken, then garnish with fresh parsley and serve immediately.