Heat 1 tablespoon of olive oil up in a skillet over medium heat . Add the shallots and saute until they are tender. Season the chicken and add it to the skillet. Brown the chicken until it is cooked through. Turn the heat down to medium, add the zucchini and cover. Allow the zucchini to steam until tender.
Meanwhile, add all of the ingredients for the pesto to a food processor and pulse to combine.
Bring 5 quarts of water to a rolling boil. Salt the water generously. Add the pasta to the water and cook until al dente.
Take 2 tablespoons of the pesto and add it to the skillet with the chicken. Once the pasta has finished cooking, drain it and add the remaining pesto. Mix well and serve with the chicken mixture on top.