Fry the chicken in pesto to flavor it.
Cook the pasta and drain, reserving some of the pasta water.
Add chicken, more pesto to coat the pasta, kalamata olives, tomatoes.
Add cheese slowly and stir vigorously. Use pasta water to thin. The cheese will become saucy–this always seems like it won't work, but if you stick with stirring and use the starchy pasta water, it does.