In a large stockpot, heat the canola oil over medium-high heat.
Add the carrots and peppers and sauté for 5 minutes, stirring occasionally, until slightly tender.
Add the mushrooms and snow peas and sauté, stirring constantly, for a 2-4 minutes more.
Add the broth and increase heat to a boil.
Once boiling, reduce heat to medium-low, add chopped cooked chicken and simmer about 5 minutes, until the chicken is heated through.
Stir in coconut milk and simmer for a few more minutes.
Add lime juice, fish sauce (if using), and cilantro.
Garnish with lime slices and additional cilantro.