The possibilities to measure lepton forward--backward asymmetries at the LHC in the reaction pp(qqbar) --> l+l- are studied for dilepton events with masses above 400 GeV. It is shown that such measurements allow accurate tests of the neutral current interference structure up to about 2 TeV center of mass energies. The sensitivity of asymmetries at the LHC to new physics is demonstrated within the context of quark compositeness and exotic Z' scenarios.