Chaotic oscillator can be produced by a single piecewise-linear element connected to a linear circuit. In this paper, the process of synthesizing the piecewise-linear chaotic circuit is discussed. Firstly, The parameters of the nonlinear element and the admittance function of the one-port circuit are determined by the eigenvalues of the system. Secondly, the one-port circuit is designed according to the admittance function. The one-port circuit can be realized with two kinds of basic admittance functions in parallel. The inductance and the capacitance of the circuit are always positive, and the negative resistances are always commonly grounded. Finally, the example of synthesizing chaotic circuit with the proposed method in presented.