Time-dependent CP violation is measured in the (B-0) over bar -> J/psi pi(+)pi(-) p-channel for each pi(+)pi(-) resonant final state using data collected with an integrated luminosity of 3.0 fb(-1) in pp collisions using the LHCb detector. The final state with the largest rate, J/psi rho(0)(770), is used to measure the CP-violating angle 2 beta(eff) to be (41.7 +/- 9.6(-6.3)(+2.8)).. This result can be used to limit the size of penguin amplitude contributions to CPviolation measurements in, for example, (B-0) over bar -> J/psi pi(+)pi(-) decays. Assuming approximate SU(3) flavour symmetry and neglecting higher order diagrams, the shift in the CP-violating phase phi(s) limited to be within the interval [-1.05 degrees, + 1.18 degrees] at 95% confidence level. Changes to the limit due to SU(3) symmetry breaking effects are also discussed. (C) 2015 The Authors. Published by Elsevier B.V.