  The charge-exchange reaction K^+ Xe --> K^0 p Xe' is investigated using the
data of the DIANA experiment. The distribution of the pK^0 effective mass shows
a prominent enhancement near 1538 MeV formed by \sim 80 events above the
background, whose width is consistent with being entirely due to the
experimental resolution. Under the selections based on a simulation of K^+Xe
collisions, the statistical significance of the signal reaches 5.5\sigma. We
interpret this observation as strong evidence for formation of a pentaquark
baryon with positive strangeness, \Theta^+(uudd\bar{s}), in the charge-exchange
reaction K^+ n --> K^0 p on a bound neutron. The mass of the \Theta^+ baryon is
measured as m(\Theta^+) = 1538+-2 MeV. Using the ratio between the numbers of
resonant and non-resonant charge-exchange events in the peak region, the
intrinsic width of this baryon resonance is determined as \Gamma(\Theta^+) =
0.34+-0.10 MeV.
