The charge-exchange reaction K+Xe→K0pXe′ is investigated using the data of the DIANA experiment. The distribution of the pK0 effective mass shows a prominent enhancement near 1538 MeV formed by nearly 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 5.5σ. We interpret this observation as strong evidence for formation of a pentaquark baryon with positive strangeness, Θ+(uudds¯), in the charge-exchange reaction K+n→K0p on a bound neutron. The mass of the Θ+ baryon is measured as m(Θ+)=1538±2 MeV. Using the ratio between the numbers of resonant and nonresonant charge-exchange events in the peak region, the intrinsic width of this baryon resonance is determined as Γ(Θ+)=0.34±0.10 MeV.