Place a large skillet over medium-high heat. Melt the butter in the skillet.
Add the onion slices and cook until the onions begin to brown, about 5 to 8 minutes. Reduce the heat to medium and continue to cook for another 10 to 15 minutes until the onions have caramelized and are soft & golden brown.
While the onions are cooking, bring a large pot of water to a boil and season the water generously with salt.
Add your pasta to the water and cook according to package directions until al dente. Drain the pasta and immediately douse the pasta in cold water to stop the cooking and cool it down. Drain the pasta.
Pour the pasta into a large mixing bowl. Add the caramelized onions, chicken, and cheese. Toss to combine.
Pour the dressing over the ingredients in the bowl, and gently mix until everything is well coated. Cover the bowl and refrigerate until ready to serve (up to 6 hours ahead of time). You could serve this pasta salad as soon as everything is mixed if you don't mind things being warm.
You could save yourself a little cooking time by using 1/2 of a rotisserie chicken from the store for the chicken in this recipe. Just shred the meat and you're all set!