Cook the rotini pasta in a large pot of salted boiling water until al dente, according to package instructions. Drain and rinse to stop the cooking process and keep the pasta from sticking to each other.
Make the dressing by combining all ingredients in a measuring cup or small bowl.
Place the cooked pasta, shredded chicken, tomatoes, onion, mozzarella, olives, avocado, and chopped parsley in a large salad bowl.
Drizzle the dressing on top and toss to coat. Refrigerate at least 30 minutes before serving.