Rinse collard greens and tear leaves from center ribs; discard center ribs and stems.
Pour oil into a 12- to 14-inch frying pan over medium-high heat; when hot, add onion and garlic and stir frequently until onion is limp, 5 to 8 minutes. Stir in balsamic vinegar, brown sugar, raisins, pine nuts, and collard greens. Stir frequently until greens are slightly wilted, 3 to 4 minutes. Reduce heat, cover, and cook until greens are very wilted and tender to bite, about 15 minutes. Add salt and pepper to taste; serve at once.