We introduce and study the critical properties of the triplet XY quantum chain. This system is described in terms of three-spin interactions and is the generalization of the standard XY quantum chain. We show that this model, with periodic boundaries, has a local gauge invariance and can be described by the composition of two triplet Ising models, with general toroidal boundary conditions. From this composition the phase diagram as well the conformal anomaly and critical exponents are determined by exploring their relations with the mass gap amplitudes predicted by conformal invariance.