  We study the fate of spin-1/2 spiral-ordered two-dimensional quantum
antiferromagnets that are disordered by quantum fluctuations. A crucial role is
played by the topological point defects of the spiral phase, which are known to
have a Z2 character. Previous works established that a nontrivial quantum
spin-liquid phase results when the spiral is disordered without proliferating
the Z2 vortices. Here, we show that when the spiral is disordered by
proliferating and condensing these vortices, valence-bond solid ordering occurs
due to quantum Berry phase effects. We develop a general theory for this latter
phase transition and apply it to a lattice model. This transition potentially
provides a new example of a Landau-forbidden deconfined quantum critical point.
