Bring a large pot of water to a boil and cook the peas according to the package directions. Transfer the peas to a bowl using a slotted spoon. Add the pasta to the water and cook according to the package directions. Drain the pasta and return it to the pot. Add the oil and toss. Place the pasta in a large glass bowl. Sprinkle the peas evenly over the pasta. Add the chicken in a single layer, then add the spinach and tomatoes. Serve the dressings on the side.