In a large pot, heat oil until hot and brown chicken pieces on all sides. Remove chicken temporarily.
In the same frying pan, add the onions and stir until soft and slightly brown. Add the tomato paste and salt, and stir well.
Add all the prepared vegetables and fish sauce to the pot. Return the chicken to the pot and add just enough water to cover. Bring to a boil, stir, and reduce heat to medium. Simmer for approximately 30 minutes. Check the vegetables to avoid overcooking, removing them in a bowl as they are done.
When all the vegetables are cooked and removed from the stew, add the peanut butter, 1 tablespoon at a time to make sure it is well dissolved in the broth. Add the pepper, if using and simmer until broth thickens, about 20 to 30 minutes.
Return all the vegetables to the pot and simmer 5 minutes more.
Serve over white rice.