Sauté the onion, celery and garlic in butter in a medium saucepan over a moderate heat for 5 minutes, until softened. Add the flour and cook for 1 minute. Pour in the stock and bring to a simmer.
Add the carrots and chicken breast fillets, then reduce heat to low and cook gently for 15 minutes. Remove the cooked chicken and shred with forks, then return to the saucepan. Add the peas, cook for 1 minute, then turn off the heat.
Meanwhile, cook the soba noodles in a large saucepan of rapidly-boiling salted water for 4 minutes, until just tender, then drain and arrange in bowls. Top with the chicken soup.
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