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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-3/2baryons, $P_{33}$, $D_{33}$, $D_{13}$ and $P_{13}$, group intohigher-dimensional chiral multiplets $(1, \half)\oplus (\half,1)$ with a mirrorassignment. With an effective $SU(2)_R\times SU(2)_L$ Lagrangian, we deriveconstraints imposed by chiral symmetry together with the mirror assignment onthe masses and coupling constants of the quartet. Using the effectiveLagrangian, we try to find a set of baryons suitable for the chiral quartet. Itturns out that two cases reasonably agree with the mass pattern of the quartet:($\Delta(1600)$, $\Delta(1940)$, $N(1520)$, $N(1720)$) and ($\Delta(1920)$,$\Delta(1940)$, $N(2080)$, $N(1900)$).

Quartet of spin-3/2 baryons in chiral multiplet $(1, 1/2) \oplus (1/2, 1) $ with mirror assignment