Season the sliced chicken breast generously with salt and pepper.
In a large (5-6 quart) soup pot, heat the coconut oil over high heat and add the chicken breast. Stir-fry over high heat for 4-5 minutes, or until the chicken is no longer pink on the outside.
Add the sliced onion, minced garlic, and minced ginger. Continue to stir-fry for another 2-3 minutes.
Add the diced zucchini and cubed pumpkin, then stir.
Add the sliced bell pepper, sliced chili or jalapeño pepper, coconut milk, chicken broth, and lime juice. Give everything another good stir.
Bring to a boil, then lower the heat, cover, and allow to simmer for about 20 minutes, or until the pumpkin is fully cooked.
Remove from heat and season with additional salt and pepper, if desired. Garnish with cilantro leaves to serve.