Cook the pasta in a large pot of salted boiling water until al dente, following the package directions. Drain thoroughly and set aside.

In the same pot, place the chicken and add enough cold water to cover it by about an inch. Bring to a boil over high heat, then lower the heat to medium-low. Cook uncovered for 7-8 minutes, or until the chicken is no longer pink in the center. Drain the water and let the chicken cool. Once cooled, cut the chicken into ½-inch wide strips.

Prepare the pesto sauce by combining the basil leaves, olive oil, Parmesan cheese, 2 tablespoons of water, lemon juice, salt, and pepper in a food processor. Blend until the mixture is smooth, which should take about 1 minute.

In a large bowl, mix the cooked pasta, chicken strips, arugula, grape tomatoes, pecans, and the freshly prepared pesto sauce. Toss everything together until the ingredients are evenly coated.

Transfer the pasta salad to a serving bowl. If desired, sprinkle with freshly ground black pepper and drizzle with additional olive oil before serving.