A measurement of the total ppcross section at the LHC at root s = 8TeV is presented. An integrated luminosity of 500 mu b(-1) was accumulated in a special run with high-beta* beam optics to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable t. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the -t range from 0.014 GeV2 to 0.1 GeV2 to extrapolate t -> 0, the total cross section, sigma(tot)( pp -> X), is measured via the optical theorem to be sigma(tot)(pp -> X) = 96.07 +/- 0.18 (stat.) +/- 0.85 (exp.) +/- 0.31 (extr.) mb, where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation t -> 0. In addition, the slope of the exponential function describing the elastic cross section at small t is determined to be B = 19.74 +/- 0.05 (stat.) +/- 0.23 (syst.) GeV-2.