Bring a large pot of salted water to a boil and cook the chickpea pasta according to package directions until al dente, typically 7 to 9 minutes.
Drain the pasta and immediately rinse under cold running water to stop the cooking process and lower the temperature.
In a small bowl, whisk together the basil pesto, Greek yogurt, and lemon juice until the mixture is emulsified and smooth.
In a large mixing bowl, combine the cooled pasta, cubed chicken breast, halved cherry tomatoes, chopped baby spinach, and diced red onion.
Add the pesto dressing to the large bowl and toss all ingredients until the pasta and vegetables are evenly coated.
Incorporate the grated Parmesan cheese and toasted pine nuts, then season with salt and black pepper to taste.
Chill in the refrigerator for at least 30 minutes before serving to allow flavors to meld, or serve immediately at room temperature.