  We study the possible existence of chiral partners in the spin-$\thalf$
sector of the baryon spectrum. We consider a quartet scheme where four spin-3/2
baryons, $P_{33}$, $D_{33}$, $D_{13}$ and $P_{13}$, group into
higher-dimensional chiral multiplets $(1, \half)\oplus (\half,1)$ with a mirror
assignment. With an effective $SU(2)_R\times SU(2)_L$ Lagrangian, we derive
constraints imposed by chiral symmetry together with the mirror assignment on
the masses and coupling constants of the quartet. Using the effective
Lagrangian, we try to find a set of baryons suitable for the chiral quartet. It
turns out that two cases reasonably agree with the mass pattern of the quartet:
($\Delta(1600)$, $\Delta(1940)$, $N(1520)$, $N(1720)$) and ($\Delta(1920)$,
$\Delta(1940)$, $N(2080)$, $N(1900)$).
