Time-dependent CP violation is measured in the B(---)0→J/ψπ+π- channel for each π+π- 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/ψρ0(770), is used to measure the CP-violating angle 2βeff to be (41.7±9.6-6.3+2.8)°. This result can be used to limit the size of penguin amplitude contributions to CP violation measurements in, for example, B(---)s0→J/ψϕ decays. Assuming approximate SU(3) flavour symmetry and neglecting higher order diagrams, the shift in the CP-violating phase ϕs is limited to be within the interval [-1.05°, +1.18°] at 95% confidence level. Changes to the limit due to SU(3) symmetry breaking effects are also discussed.