In a large pot of lightly salted boiling water, cook the spirals according to package directions.
Add carrots to pasta during last 3 minutes of cooking.
Before draining the pasta, dip a measuring cup into the cooking water and measure out ¾ cup of the water; set aside.
Drain the pasta and carrots, rinse, and transfer to a large serving bowl. Add the chicken and set aside.
Place remaining ingredients in a food processor or blender container and process or blend until smooth.
Drizzle peanut butter mixture over pasta and chicken, tossing well.