Heat olive oil in a large pan over medium heat. Add shallots, zucchini, fennel, and garlic and sauté for 8 to 10 minutes or until slightly softened.
Season with salt and stir.
Add chicken breasts on top of vegetables and cover with broth, wine, and dill. Bring to a boil, then reduce to a simmer until chicken is cooked, about 15 minutes.
Remove chicken and vegetables and set aside, discarding dill. Boil liquid for 8 to 10 minutes or until slightly reduced.
Slice chicken and place on a serving platter with vegetables. Pour sauce over top and serve immediately.