Preheat the oven to 350°F.
Pat the chicken breasts dry and season with salt and pepper. Roast on a baking sheet until cooked through, about 22-28 minutes. Let rest for 5 minutes before dicing.
Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions. Drain the pasta, return to the pot, and drizzle with olive oil to prevent sticking.
In a food processor, blend the basil, arugula, garlic, parmesan, olive oil, pine nuts, lemon juice, salt and pepper until smooth.
Toss the pasta, roasted red peppers, and diced chicken with the pesto sauce until evenly coated.
Divide the pesto pasta and chicken between plates and top with roasted red peppers, pine nuts and parmesan.