Snap the ends off the green beans, and then cut into 1-inch segments.
Melt the butter in a large saucepan. Add the onion, and sauté until it becomes translucent.
Add potato, carrot, green beans, kidney beans, salt, pepper, and chicken stock. Bring to a boil, and simmer for at least 1 hour. Longer cooking will make the vegetables more tender and enhance the flavors, but 1 hour is the minimum cooking time.
If desired, fork-mash the vegetables before serving.