We are not aware of any study trying to use the polynomial chaos framework to find a closed form solution for the LQR problem in this framework, i.e., a solution that would depend on the number of terms in the polynomial chaos expansions and that would numerically converge to the solution of the problem as S→∞. The original intent of the work presented here was to try deriving such a solution, but this proved to be extremely difficult, if not impossible. However, an efficient numerical method to solve this problem could be derived instead. Polynomial chaos based methods have the advantage of computationally much more efficient than Monte Carlo simulations. The method presented in this article treats the LQR problem as an optimality problem using Lagrange multipliers in an extended form associated with the polynomial chaos framework, and uses an iterative algorithm that converges to the optimal answer. Therefore, it goes at the root of the solution of the LQR problem, which is derived using Lagrange multipliers in the deterministic case, which leads to the well-known algebraic Riccati equations. Therefore, the method presented in this article might have the potential of being a first step towards the development of computationally efficient numerical methods for H_∞ design with parametric uncertainties.