  A free semigroup algebra S is the weak-operator-closed (non-self-adjoint)
operator algebra generated by n isometries with pairwise orthogonal ranges. A
unit vector x is said to be wandering for S if the set of images of x under
non-commuting words in the generators of S is orthonormal.
  We establish the following dichotomy: either a free semigroup algebra has a
wandering vector, or it is a von Neumann algebra. Consequences include that
every free semigroup algebra is reflexive, and that certain free semigroup
algebras are hyper-reflexive with a very small hyper-reflexivity constant.
