Heat the olive oil in a soup pot over medium-high heat. Add the garlic, potatoes and onions, and season with salt and pepper. Partially cover the pot and cook to soften, 8 to 10 minutes. Add the green beans, stock, chicken and tomatoes, and bring to a simmer. Taste and adjust the seasoning.
Cool and store for a make-ahead meal. Reheat over medium heat. To serve, add the lemon zest, lemon juice and tarragon. Serve the soup with warm bread.
Place the chicken in a pot over a bed of bay leaves, garlic, celery, parsley, carrots and onions. Sprinkle with salt and fill the pot with water to cover the chicken. Sprinkle in a few peppercorns. Bring the water to a boil, then reduce to a simmer and cook 45 minutes, turning occasionally. Turn off the heat and cool the chicken in the broth. Separate the meat from the bones and skin. Reserve the meat and discard the bones and skin. Strain the stock.