The decay Bc(+) -> J/psi pi(+) pi(-) pi(+) is observed for the first time, using 0.8 fb(-1) of pp collisions at root s = 7 TeV collected by the LHCb experiment. The ratio of branching fractions B(B-c(+) -> J/psi pi(+) pi(-) pi(+))/B(B-c(+) -> J/psi pi(+)) is measured to be 2.41 +/- 0.30 +/- 0.33, where the first uncertainty is statistical and the second is systematic. The result is in agreement with theoretical predictions.