  We study a spin system with two- and four-spin exchange interactions on the
triangular lattice, which is a possible model for the nuclear magnetism of
solid $^3$He layers. It is found that a novel spin structure with scalar chiral
order appears if the four-spin interaction is dominant. Ground-state properties
are studied using the spin-wave approximation. A phase transition concerning
the scalar chirality occurs at a finite temperature, even though the
dimensionality of the system is two and the interaction has isotropic spin
symmetry. Critical properties of this transition are studied with Monte Carlo
simulations in the classical limit.
