Remove the skin from the chicken and cut into pieces. Rinse the pieces and place in a large saucepan. Add the chicken broth and bring to a boil over medium-high heat. Pour boiling water over the tomatoes, peel them, and add whole to the pot. Reduce heat to low, cover, and simmer for 40 minutes or until the chicken reaches 74°C / 165°F at the thickest part.
After 30 minutes of simmering, stir in the peanut butter. Season with salt, pepper, and rosemary to taste.
While the chicken cooks, prepare the zucchini: clean, remove the flowers and stem base, wash, and cut into small cubes. Add to the saucepan after 30 minutes of simmering (10 minutes before the end of cooking). Stir well and season to taste again.
Serve with rice, couscous, or steamed semolina as a side dish.