Melt coconut oil in a large pot over medium-low heat. Stir in the onions, garlic, peppers, carrots and ginger with a pinch of salt and pepper. Cook until the vegetables have slightly softened, about 5 minutes.
Stir in the curry paste and cook for 5 minutes, stirring occasionally, scraping the bottom.
Stir in the chicken stock, coconut milk, snap peas and chicken. Increase heat and bring the mixture to a boil, then reduce the heat to low, cover and cook for 5 minutes.
Toss in the zoodles from one or two zucchini (add as much as you like). Serve soup immediately garnished with green onions, cilantro and a lime wedge.