  The QCD sum rule method is formulated for the strangeness +1 pentaquark
baryon with isospin I=0 and spin-parity J^P = 3/2^\pm. The spin-3/2 states are
considered to be narrower than the spin-1/2 ones, and thus may provide a
natural explanation for the experimentally observed narrow width of \Theta^+.
In order to obtain reliable results in QCD sum rule calculations, we stress the
importance of establishing a wide Borel window, where convergence of the
operator product expansion and sufficient low-mass strength of the spectral
function are guaranteed. To this end, we employ the difference of two
independent correlators so that the high-energy continuum contribution is
suppressed. The stability of the physical quantities against the Borel mass is
confirmed within the Borel window. It is found that the sum rule gives positive
evidence for the (I, J^P) = (0, 3/2^+) state with a mass of about 1.4 \pm 0.2
GeV, while we cannot extract any evidence for the (0, 3/2^-) state.
