We report a measurement of the exclusive production of pairs of charged pions in proton-proton collisions, dominated by the process pp → p(*)π+π-p(*), where p(*) stands for a diffractively dissociated proton, the π+π- pair is emitted at central rapidities y, and the incident protons stay intact or dissociate without detection p(*). The measurement is performed with the CMS detector at the LHC, using a data sample corresponding to an integrated luminosity of 450 μb-1 collected at a center-of-mass energy of √s = 7 TeV in 2010. The cross section measured in the phase space defined by pion transverse momentum pT > 0.2 GeV/c and rapidity |y| < 2 is found to be 20.5 ± 0.3 (stat) (± 3.1 syst) ± 0.8 (lumi) μb. The differential cross sections for π+π- pairs as a function of the pion pair invariant mass, pT, and y, as well as a single-pion differential cross section as a function of pion pT are also measured and compared to several phenomenol. predictions.