For the Chicken: Season the chicken breasts on both sides with salt and pepper.
Heat 2 tablespoons of olive oil on medium-high heat and sear the chicken breasts on both sides until golden browned and cooked throughout.
Add in the chicken stock, cover with a lid and cook over medium heat for 1 hour or until the chicken easily shreds apart.
Using two forks pull the chicken apart until shredded.
Add the carrots, celery, salt, and pepper and simmer over low heat. Keep warm.
For the Matzo Balls: In a large bowl combine all of the ingredients until they are well mixed together and set in the refrigerator for at least 1 hour.
Remove the matzo ball mixture and roll into small golf ball-sized balls and place them on a sheet tray lined with parchment paper. Note: If the matzo balls become sticky while making them, dip your hands in water before rolling.
Place a few matzo balls into the soup and cook over low heat for 15 to 20 minutes or until they are cooked throughout and firm. Move the balls around and flip them over every 3-4 minutes.
Place the cooked matzo balls in a soup bowl along with the chicken broth, chopped chicken and vegetables and garnish with chopped dill and sliced green onions.