The ordering of the one-dimensional Heisenberg spin glass interacting via the long-rangepower-law interaction is studied by Monte Carlo simulations. Particular attention is paid to thepossible occurrence of ‘spin–chirality decoupling’ for appropriate values of the power-law exponentσ. Our result suggests that, for intermediate values ofσ, the chiral-glass order occurs at finite temperatures while the standard spin-glass orderoccurs only at zero temperature.