The dependence of the rate of proton-proton interactions on the centre-of-mass collision energy, root s, is of fundamental importance for both hadron collider physics and particle astrophysics. The dependence cannot yet be calculated from first principles; therefore, experimental measurements are needed. Here we present the first measurement of the inelastic proton-proton interaction cross-section at a centre-of-mass energy, root s, of 7 TeV using the ATLAS detector at the Large Hadron Collider. Events are selected by requiring hits on scintillation counters mounted in the forward region of the detector. An inelastic crosssection of 60.3 +/- 2.1 mb is measured for xi > 5x10(-6), where xi is calculated from the invariant mass, M(X), of hadrons selected using the largest rapidity gap in the event. For diffractive events, this corresponds to requiring at least one of the dissociation masses to be larger than 15.7 GeV.