The uncertainty quantification for a flexible flapping airfoil was investigated using the point-collocation non-intrusive polynomial chaos method. The chordwise flexible amplitude was assumed to obey a normal distribution. It is observed that the time-averaged thrust coefficient obeys a Gauss-like but not the exact Gauss distribution, while the probability of the propulsive efficiency is much different from the exact Gauss distribution. The effect of the chordwise flexure on the time-averaged thrust coefficient is much larger than the effect on the propulsive efficiency. This work could be a preparation for the robust design of a flexible flapping wing with respect to a stochastic chordwise flexure.