Place a saucepot filled halfway with water to a boil and set a bowl nearby filled with ice. Once boiling, add in the beet noodles and greens (optional) and cook for 1-2 minutes or until slightly softened. Drain into a colander and immediately set over ice to stop the cooking process. Pat dry once cooled.
While the beets cool, place all of the ingredients for the yogurt-dill sauce into a bowl and whisk together. Set aside.
Place the chicken, beet noodles and beet greens (optional) into a large mixing bowl, add the yogurt-dill sauce and toss together to combine.
Plate the salad and garnish with any additional dill, if desired.