Bring a pot of salted water to a boil. Add the pasta and cook as the label directs. Drain and rinse under cold water to stop the cooking.
Meanwhile, whisk the yogurt, mayonnaise, 1/4 cup water, the vinegar, mustard, dill, chives and 2 teaspoons salt in a medium bowl. Remove the skin from the chicken and shred the meat into large pieces. Add the chicken, celery and cucumber to the dressing and gently stir to combine.
Shake the excess water from the pasta and add it to the chicken salad. Season with pepper and toss. Serve over the greens.