  We investigate the non-Gaussianities of inflation driven by a single scalar
field coupling non-minimally to the Einstein Gravity. We assume that the form
of the scalar field is very general with an arbitrary sound speed. For
convenience to study, we take the subclass that the non-minimal coupling term
is linear to the Ricci scalar $R$. We define a parameter
$\mu\equiv\epsilon_h/\epsilon_\theta$ where $\epsilon_h$ and $\epsilon_\theta$
are two kinds of slow-roll parameters, and obtain the dependence of the shape
of the 3-point correlation function on $\mu$. We also show the estimator
$F_{NL}$ in the equilateral limit. Finally, based on numerical calculations, we
present the non-Gaussianities of non-minimal coupling chaotic inflation as an
explicit example.
