Heat olive oil in a skillet over medium-low heat. Add shallot and cook until soft and translucent, 3 to 5 minutes. Add garlic and cook until fragrant, about 30 seconds. Add chanterelle mushrooms and saute for 10 minutes. Stir together cornstarch and water in a bowl and add to mushrooms. Mix well.
Add zucchini to the skillet and season with salt and pepper. Cook until zucchini are soft, about 20 minutes.