  Taking into account that the scalar $a_0(980)$ can be dynamically generated
from the pseudoscalar-pseudoscalar interaction within the chiral unitary
approach, we have studied the single Cabibbo-suppressed process $D^+\to
\pi^+\pi^0\eta$. We find clear peaks of $a_0(980)^+$ and $a_0(980)^0$ in the
$\pi^+\eta$ and $\pi^0\eta$ invariant mass distributions, respectively. The
predicted Dalitz plots of $D^+\to \pi^+\pi^0\eta$ also manifest the significant
signals for $a_0(980)^+$ and $a_0(980)^0$ states. The uncertainties of the
results due to the free parameters are also discussed. Our study shows that the
process $D^+\to \pi^+\pi^0\eta$ can be used to explore the nature of the scalar
$a_0(980)$, thus we encourage the experimental physicists to measure this
reaction with more precision.
