Heat 1 tablespoon of extra-virgin olive oil in a skillet over medium heat. Add the chicken breast and cook until golden brown and fully cooked through, about 5-7 minutes per side. Remove the chicken from the skillet and allow it to rest for a few minutes before dicing into bite-sized pieces. I like to let the chicken rest before cutting to keep it juicy.
Bring a large pot of salted water to a boil. Add the penne or rotini pasta and cook according to package instructions until al dente, usually about 8-10 minutes. Drain the pasta well but do not rinse; you want the surface starch to help the dressing stick.
While the chicken and pasta are cooling slightly, halve the cherry tomatoes, chop the cucumber, and mince the red onion. Place the cherry tomatoes, chopped cucumber, and minced red onion into a large mixing bowl.
To the bowl with the vegetables, add the drained pasta from Step 2, diced chicken from Step 1, crumbled feta cheese, and pitted kalamata olives. Gently toss everything together so that the ingredients are evenly distributed.
Drizzle the remaining 2 tablespoons of extra-virgin olive oil evenly over the salad and toss gently to coat. Taste the salad and adjust seasoning if needed. I like to chill the salad before serving, as it blends the flavors nicely.