  A first measurement of the inelastic cross-section is presented for
proton-proton collisions at a center of mass energy sqrt{s}=7 TeV using the
ATLAS detector at the Large Hadron Collider. In a dataset corresponding to an
integrated luminosity of 20 mub-1, events are selected by requiring hits on
scintillation counters mounted in the forward region of the detector. An
inelastic cross-section of $60.3 +/- 2.1 mb is measured for xi > 5x10^-6, where
xi=M_X^2/s 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.
