Phase transitions and critical phenomena have been clarified for an XY model on the triangular lattice of ultra-thin magnetic films. We have calculated the ther modynamic quantities such as the internal energy, the specific heat, the chirali ty and so on by using Monte-Carlo simulations. The critical behaviours have been clarified by using finite-size scaling analyses. We have found a new critical b ehaviour due to a steep increase of the chirality as a function of temperature f or the XY model on a layered triangular lattice with antiferromagnetic layers an d ferromagnetic layers in some range of interaction parameters, besides the Kost erlize-Thouless transition and the usual chirality transition. In the new chiral ity transition, the value of a critical exponent has not been observed over any thickness dependence of this value as far as the layered systems are concerned. In the other chirality transition, the value of a critical exponent has been obs erved over the thickness.