Using event-by-event hydrodynamic calculations, we find that the fluctuations of the elliptic flow (v(2)) in the reaction plane have a negative skew. We compare the skewness of v(2) fluctuations to that of initial eccentricity fluctuations. We show that skewness is the main effect lifting the degeneracy between higher-order cumulants, with negative skewcorresponding to the hierarchy v(2){4} > v(2){6} observed inPb+ Pb collisions at theCERNLarge Hadron Collider. We describe how the skewness can be measured experimentally and show that hydrodynamics naturally reproduces its magnitude and centrality dependence.