Heat the oil in a large skillet over medium heat. Add the onion, garlic, chili powder, and cumin and sauté until onions are soft. Add the tomatoes and 1 cup of water. Bring to a simmer, partially cover with a lid, and cook 10 minutes. Add the beans and return to a simmer; continue cooking, uncovered, 20 minutes, until the chili is thick. Remove from heat and stir in the vinegar. Season to taste with salt and freshly ground pepper.
While the chili cooks, prepare the polenta according to package directions (5 to 8 minutes), and stir in the butter. Season to taste with salt and freshly ground pepper. Divide between 4 bowls and ladle chili over top. Spoon a little salsa on top, if desired.