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Place the whole chicken, carrots, celery, onion, dill, and water in a large pot. Bring to a boil, then reduce to a gentle simmer. Skim off any foam that rises to the top.
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Simmer uncovered for 1 hour until the broth is rich and golden. Remove the chicken and shred the meat, discarding skin and bones. Strain the broth and return it to the pot.
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Make the matzo balls: In a bowl, mix matzo meal, beaten eggs, schmaltz, seltzer water, and 1 teaspoon salt. Stir until combined. Cover and refrigerate for 30 minutes.
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Bring a large pot of salted water to a gentle boil. With wet hands, roll the matzo mixture into balls about 1.5 inches in diameter.
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Drop the matzo balls into the simmering water. Cover with a tight lid and do not lift it for 30 minutes. The steam is what makes them fluffy.
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Add the shredded chicken and sliced carrots back to the broth. Ladle the broth over the cooked matzo balls in bowls and garnish with fresh dill.