Put the pesto in a large bowl.
Cook the pasta according to package instructions.
Drain the pasta and reserve 1/3 cup of the pasta water.
Whisk the pasta water into the pesto.
While the pasta is cooking, heat the oil in a large skillet over medium-high heat. Add the garlic and cook, stirring until soft and fragrant, about 30 seconds.
Add the chicken, peppers, and olives and cook, stirring until hot, about 3 minutes. Season with salt and pepper.
Add the pasta and cheese to the pesto and toss to combine.
Add the chicken mixture and combine.
Divide the pasta among 4 bowls and serve immediately.
Sprinkle parmesan, freshly ground black pepper to taste.