  Superfluidity ordering of thin ^3He films is studied by Monte Carlo
simulations based on a two-dimensional lattice spin model with Z_2\times
U(1)\times SO(3) symmetry. Successive phase transitions with an intermediate
`chiral' phase, in which the l-vector aligns keeping the phase of the
condensate disordered, is found. Possible experiments to detect the successive
transitions are discussed.
