In a large pot, heat the olive oil over medium heat. Add the minced yellow onion and garlic, sautéing until fragrant and translucent, about 3-4 minutes. Add the chicken breasts, followed by the chicken stock, diced carrots, diced celery, and half of the chopped dill. Season with salt and pepper. Bring to a boil, then reduce to a simmer. Cook for about 20-25 minutes, or until the chicken is cooked through.
Once cooked, remove the chicken breasts from the pot and let them cool slightly. Shred the chicken into bite-sized pieces and return it to the pot.
In a mixing bowl, whisk together the eggs and melted schmaltz. In another bowl, combine the matzo meal, baking powder, and a pinch of salt. Gradually mix the dry ingredients into the egg mixture until just combined. Cover and refrigerate for 30 minutes.
Once the mixture has chilled, wet your hands with water and form the mixture into balls about the size of a walnut. This will help prevent sticking.
Bring the soup back to a gentle boil. Carefully drop the matzo balls into the simmering broth. Cover the pot and let them cook for 20-25 minutes, or until they have doubled in size.
Once the matzo balls are cooked through, stir in the remaining dill and adjust seasoning with salt and pepper if needed. If desired, add sliced green onions for a fresh touch.