The decay B(c)(+) → J/ψπ(+) π(-) π(+) is observed for the first time, using 0.8 fb(-1) of pp collisions at sqrt[s] = 7 TeV collected by the LHCb experiment. The ratio of branching fractions B(B(c)(+) → J/ψπ(+) π(-) π(+))/B(B(c)(+)→J/ψπ^{+}) 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.