  We propose a mechanism of a vector chiral long-range order in two-leg
spin-1/2 and spin-1 antiferromagnetic ladders with four-spin exchanges and a
Zeeman term. It is known that for one-dimensional quantum systems, spontaneous
breakdown of continuous symmetries is generally forbidden. Any vector chiral
order hence does not appear in spin-rotationally [SU(2)]-symmetric spin
ladders. However, if a magnetic field is added along the S^z axis of ladders
and the SU(2) symmetry is reduced to the U(1) one, the z component of a vector
chiral order can emerge with the remaining U(1) symmetry unbroken. Making use
of Abelian bosonization techniques, we actually show that a certain type of
four-spin exchange can yield a vector chiral long-range order in spin-1/2 and
spin-1 ladders under a magnetic field. In the chiral-ordered phase, the Z_2
interchain-parity (i.e., chain-exchange) symmetry is spontaneously broken. We
also consider effects of perturbations breaking the parity symmetry.
