  We investigate the quantum three spin model $({\bf S_1},{\bf S_2},{\bf S_3})$
of spin$=1/2$ on a triangle, in which spins are coupled with
lattice-vibrational modes through the exchange interaction depending on
distances between spin sites. The present model corresponds to the dynamic
Jahn-Teller system $E_g\otimes e_g$ proposed by Longuet-Higgins {\it et al.},
Proc.R.Soc.A.{\bf 244},1(1958). This correspondence is revealed by using the
transformation to Nakamura-Bishop's bases proposed in Phys.Rev.Lett.{\bf
54},861(1985). Furthermore, we elucidate the relationship between the behavior
of a chiral order parameter ${\hat \chi}={\bf S_1\cdot(S_2\times S_3)}$ and
that of the electronic orbital angular momentum ${\hat \ell_z}$ in $E_g\otimes
e_g$ vibronic model: The regular oscillatory behavior of the expectation value
$<{\hat \ell_z}>$ for vibronic structures with increasing energy can also be
found in that of $<{\hat \chi}>$. The increase of the additional
anharmonicity(chaoticity) is found to yield a rapidly decaying irregular
oscillation of $<{\hat \chi}>$.
