In a large straight-sided skillet, combine the bacon, onion, and oil over medium heat. Cook, stirring occasionally, until onions are translucent and bacon renders some of its fat, about 3 minutes. Season with salt and pepper. Add the vinegar, and cook until it evaporates, about 30 seconds.
Add the collard greens and chicken stock. Bring liquid to a simmer, stirring occasionally. Cover, and cook 15 minutes.