In an 8-quart casserole stockpot, heat 2 tablespoons of the oil over medium high heat. Add the flour to a shallow bowl and season with about 1 teaspoon each of kosher salt and pepper. Dredge the chicken in the flour, shake off the excess.
Place half of the chicken in the stockpot but do not overcrowd. Cook until golden, about 2 minutes per side then transfer the chicken to a bowl. Brown the remaining chicken in 2 more tablespoons of the oil.
Add the remaining 1 tablespoon of oil and the carrots, celery and onion to the stockpot and cook over medium heat for 3 minutes. Add the sliced leek and garlic and cook for about 2 minutes and season with salt and pepper.
Add the chicken stock and water and bring to a boil. Cover and simmer over low heat, stirring occasionally for about 20 minutes.
Add the orzo and chicken to the stockpot and cover and simmer for about 10 minutes or until orzo is tender.
Stir in the lemon juice, season with salt and pepper and sprinkle with tarragon. Serve immediately.