A new algorithm is proposed for the design of nonlinear dynamical systems with probabilistic uncertainties. The dependence of the design objective and constraints on uncertainties is quantified by the polynomial chaos expansions (PCEs), while the relationships between the design parameters and the design objective/constraints are parameterized by Legendre polynomials. In two case studies, the polynomial chaos-based algorithm reduces the number of system evaluations required by optimization by an order of magnitude. Quantifying the dependence on uncertain parameters via the PCEs and including the quantification in design optimization simultaneously improved the distribution of the performance index and the probability of constraint fulfillment. (C) 2016 American Institute of Chemical Engineers