Reduced order models of high-order single-input single-output dynamical systems are derived in terms of beat Chebyshev rational approximations on a desired domain in the complex plane. An algorithm is proposed for deriving local best Chebyshev rational approximations for a complex function in the complex plane and is based on a complex version of Lawson's algorithm. The method is applied to minimizing a time response error bound of the reduced models and it is shown that the local best Chebyshev approximations are in fact frequency-response approximations. The algorithm enables the control of the rational approximation pole and zero locations and, therefore, if the given system is stable, its reduced order models can be made stable as well as minimal phase.