Abstract: We study the chi(c1) -> eta pi(+)pi(-) decay, paying attention to the production of f(0)(500), f(0)(980), and a(0)(980) from the final state interaction of pairs of mesons that can lead to these three mesons in the final state, which is implemented using the chiral unitary approach. Very clean and strong signals are obtained for the a(0)(980) excitation in the eta pi invariant mass distribution and for the f(0)(500) in the pi(+)pi(-) mass distribution. A smaller, but also clear signal for the f(0)(980) excitation is obtained. The results are contrasted with experimental data and the agreement found is good, providing yet one more test in support of the picture where these resonances are dynamically generated from the meson-meson interaction.