  In this work we study a scalar field dark matter model with mass of the order
of 100 MeV. We assume dark matter is produced in the process $e^-+e^+\to \phi
+\phi^*+\gamma$, that, in fact, could be a background for the standard process
$e^-+e^+\to \nu +\bar\nu+\gamma$ extensively studied at LEP. We constrain the
chiral couplings, $C_L$ and $C_R$, of the dark matter with electrons through an
intermediate fermion of mass $m_F=100$ GeV and obtain $C_L=0.1(0.25)$ and
$C_R=0.25(0.1)$ for the best fit point of our $\chi^2$ analysis. We also
analyze the potential of ILC to detect this scalar dark matter for two
configurations: (i) center of mass energy $\sqrt{s}=500$ GeV and luminosity
$\mathcal{L}=250$ fb$^{-1}$, and (ii) center of mass energy $\sqrt{s}=1$ TeV
and luminosity $\mathcal{L}=500$ fb$^{-1}$. The differences of polarized beams
are also explored to better study the chiral couplings.
