In a large pot of salted water, add the pasta and cook, stirring occasionally, according to the package instructions until “al dente”. Drain, rinsing quickly under cold water, and allow to cool in a large bowl.
In the meantime, wash the celery hearts removing any damaged parts, and cut them into small sticks or dice. Cut the chicken into small pieces, and add them to the pasta together with the celery.
Combine the parve pesto with the olive oil and the white vinegar, salt and pepper. Pour this dressing onto the pasta salad and stir gently.
Refrigerate until about 10 minutes before serving.