  The Floreanini-Jackiw formulation of the chiral quantum-mechanical system
oscillator is a model of constrained theory with only second-class constraints.
in the Dirac's classification.The covariant quantization needs infinite number
of auxiliary variables and a Wess-Zumino term. In this paper we investigate the
path integral quatization of this model using $G\ddot{u}ler's$ canonical
formalism. All variables are gauge variables in this formalism. The Siegel's
action is obtained using Hamilton-Jacobi formulation of the systems with
constraints.
