  The effects of symmetric helical interaction which is called the Kaplan,
Shekhtman, Entin-Wohlman, and Aharony (KSEA) interaction on the ground-state
properties of three kinds of spin chains in a transverse field have been
studied by means of correlation functions and chiral order parameter. We find
that the anisotropic transition of $XY$ chain in a transverse field ($XY$TF)
disappears because of the KSEA interaction. For the other two chains, we find
that the regions of gapless chiral phases in the parameter space induced by the
DM or $XZY-YZX$ type of three-site interaction are decreased gradually with
increase of the strength of KSEA interaction. When it is larger than the
coefficient of DM or $XZY-YZX$ type of three-site interaction, the gapless
chiral phases also disappear.
