A new method for the perturbative calculation of the correlation energy due to connected triple excitations (T) in the framework of local coupled cluster theory (LCCSD) is presented, for which all computational resources scale linearly with molecular size. The present implementation, which so Ear neglects inter-triples couplings via the off-diagonal elements of the occupied-occupied block of the Fock; matrix, recovers 80-90% of the conventional triples energy. The present LCCSD(T) method should allow to treat systems with more than 1000 basis functions and several hundred correlated electrons. Test calculations for medium sized molecules already show speedups by factors of 500-1000 as compared to the conventional (T) correction.