In this contribution we discuss the design of functional observers for polynomialsystems. Our approach is based on a high gain design employing an embed-ded observer. The functional to be estimated is generated from the high gainobserver’s state. The restriction to polynomial systems allows the representationof the system’s and the observer’s dynamics as polynomial ideals. For the calcu-lations we utilize methods from algebraic geometry. Our approach is illustratedon a chaotic system.