  We consider frustrated Heisenberg antiferromagnets, whose clean-limit ground
state is characterized by non-collinear long-range order with non-zero vector
chirality, and study the effects of quenched bond disorder, i.e., random
exchange couplings. A single bond defect is known to induce a dipolar texture
in the spin background independent of microscopic details. Using general
analytical arguments as well as large-scale simulations for the classical
triangular-lattice Heisenberg model, we show that any finite concentration of
such defects destroys long-range order for spatial dimension $d\leq 2$, in
favor of a glassy state whose correlation length in $d=2$ is exponentially
large for small randomness. Our results are relevant for a wide range of
layered frustrated magnets.
