In a large pot, heat oil over medium heat. To the oil, add the chicken and brown for 5 minutes then add the next 4 ingredients (onion through mushrooms).
Sauté the mixture for about 10 minutes, or until vegetables are starting to get tender. To the pot, add the remaining 7 ingredients (coconut milk through parsley), turn heat up to high and bring to a boil. Reduce heat to low and cover pot. Simmer soup for 30 minutes, until the vegetables are tender and chicken is cooked through. Serve warm.