  It is demonstrated that measurements of photon asymmetry in the $\gamma n \to
K^- K^+ n$ reaction, can most likely determine the parity of the newly
discovered $\Theta^+$ pentaquark. We predict that if the parity of $\Theta^+$
is positive, the photon asymmetry is significantly positive; if the parity is
negative, the photon asymmetry is significantly negative. If the background
contribution is large, the photon asymmetry may become very small in magnitude,
thereby making it difficult to distinguish between the positive and negative
parity results. However, even in this case, a combined analysis of the $(K^+
n)$ invariant mass distribution and photon asymmetry should allow a
determination of the parity of $\Theta^+$.
