Bring a large pot of water to a boil. Add fusilli pasta. Cook for 8-10 minutes or until al dente. Drain and set aside.
Bring a small pot of water to a boil. Add the sugar snap peas and blanch for 45 seconds. Immediately run sugar snap peas under cold water.
In a large bowl, add the cooked pasta, sugar snap peas, green peas, chickpeas, grape tomatoes, red onions, red peppers, salt, black pepper, and pesto. Mix until well blended.