The first double diffractive cross-section measurement in the very forward region has been carried out by the TOTEM experiment at the LHC with a center-of-mass energy of root s = 7 TeV. By utilizing the very forward TOTEM tracking detectors T1 and T2, which extend up to vertical bar eta vertical bar = 6.5, a clean sample of double diffractive pp events was extracted. From these events, we determined the cross section sigma(DD) = (116 +/- 25) mu b for events where both diffractive systems have 4.7 < vertical bar eta vertical bar(min) < 6.5.