  We compute cross sections of $\Theta^+$ production near threshold for a
polarized proton reaction, $\vec p \vec p \to \Sigma^+ \Theta^+$ which was
recently proposed to determine unambiguously the parity of $\Theta^+$. Within
theoretical uncertainties cross sections for the allowed spin configuration are
estimated; it is of order of one microbarn for the positive parity $\Theta^+$
and about 1/10 microbarn for the negative parity $\Theta^+$ in the threshold
energy region where the s-wave component dominates.
