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 sqrt[s]=7 TeV. By utilizing the very forward TOTEM tracking detectors T1 and T2, which extend up to |η|=6.5, a clean sample of double diffractive pp events was extracted. From these events, we determined the cross section σDD=(116±25) μb for events where both diffractive systems have 4.7<|η|min<6.5.