Combine vinegar and shallots in heavy small saucepan. Boil over medium heat until most vinegar is absorbed (about 1 tablespoon liquid should remain in pan), stirring frequently, about 6 minutes. Transfer mixture to small bowl; cool completely. Add butter; mix with fork until blended.
Cook beans in large pot of boiling salted water until crisp-tender, about 6 minutes. Drain. Refresh under cold water; drain. Pat dry with paper towels. (Balsamic-shallot butter and beans can be made 1 day ahead. Cover separately; chill.)
Combine beans and balsamic-shallot butter in large nonstick skillet. Toss over medium heat until beans are heated through, about 5 minutes. Season to taste with salt and pepper and serve.