  We study the $\chi_{c1} \to \eta \pi^+ \pi^-$ 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.
