Heat olive oil or butter over medium-high heat in a 4- to 5-quart pot. Add leeks, celery, and carrot (if using), salt, and pepper, and cook, stirring, until leeks have softened a bit, about 4 minutes. Add garlic and cook one minute more. Add broth, water, and chicken plus salt (I use 2 to 3 teaspoons of additional kosher salt for barely-salted stock) and many grinds of black pepper and bring to a boil. Reduce heat to medium-low and cover, simmering for 15 minutes, until chicken is very tender and cooked through.