Hydrodynamic simulations are used to make predictions for the integrated elliptic flow coefficient v2 in square root(s) = 5.5 TeV lead-lead and square root(s) = 14 TeV proton-proton collisions at the LHC. We predict a 10% increase in v2 from RHIC to Pb+Pb at LHC, and v2 approximately 0 in p+p collisions unless eta/s<0.08.