  The exclusive production of pion pairs in the process $pp\to pp\pi^+\pi^-$
has been measured at $\sqrt{s}$ = 7 TeV with the ATLAS detector at the LHC,
using 80 $\mu$b$^{-1}$ of low-luminosity data. The pion pairs were detected in
the ATLAS central detector while outgoing protons were measured in the forward
ATLAS ALFA detector system. This represents the first use of proton tagging to
measure an exclusive hadronic final state at the LHC. A cross-section
measurement is performed in two kinematic regions defined by the proton
momenta, the pion rapidities and transverse momenta, and the pion-pion
invariant mass. Cross section values of $4.8 \pm 1.0 \text{(stat.)} +
{}^{+0.3}_{-0.2} \text{(syst.)}\mu$b and $9 \pm 6 \text{(stat.)} +
{}^{+2}_{-2}\text{(syst.)}\mu$b are obtained in the two regions; they are
compared with theoretical models and provide a demonstration of the feasibility
of measurements of this type.
