  We present a study of the magnetic susceptibility in carefully detwinned
La_{2-x}Sr_{x}CuO_4 single crystals in the lightly-doped region (x=0-0.03),
which demonstrates a remarkable in-plane anisotropy of the spin system. This
anisotropy is found to persist after the long-range antiferromagnetic (AF)
order is destroyed by hole doping, suggesting that doped holes break the AF
order into domains in which the spin alignment is kept essentially intact. It
turns out that the freezing of the spins taking place at low temperatures is
also notably anisotropic, implying that the "spin-glass" feature is governed by
the domain structure as well.
